{"id":5377,"date":"2013-05-02T14:30:01","date_gmt":"2013-05-02T06:30:01","guid":{"rendered":"http:\/\/www.andrewsun.net\/panta_rhei\/?p=5377"},"modified":"2020-02-04T23:45:18","modified_gmt":"2020-02-04T15:45:18","slug":"fourier%e5%8f%98%e6%8d%a2%ef%bc%88%e4%b8%89%ef%bc%89","status":"publish","type":"post","link":"https:\/\/www.andrewsun.net\/panta_rhei\/archives\/5377","title":{"rendered":"Fourier\u53d8\u6362\uff08\u4e09\uff09"},"content":{"rendered":"<div class=\"kcite-section\" kcite-section-id=\"5377\">\n<p>[mathjax]<br \/>\n\u901a\u8fc7\u4e0a\u4e00\u7bc7\u6211\u4eec\u5df2\u7ecf\u5b66\u4f1a\u600e\u6837\u901a\u8fc7Fourier\u53d8\u6362\u91cd\u6784\u5e94\u53d8\u548c\u5e94\u529b\u7684\u6ce2\u5f62\u3002\u81f3\u5c11<i>I<\/i><sub><i>n<\/i>\/1<\/sub>\u662f\u5df2\u7ecf\u53ef\u4ee5\u76f4\u63a5\u7528Fourier\u53d8\u6362\u7684\u7ed3\u679c\u8ba1\u7b97\u4e86\u3002\u672c\u6587\u5148\u4ecb\u7ed3\u5b9e\u9645\u5b9e\u9a8c\u6570\u636e\u7684\u5bfc\u5165\uff0c\u518d\u7ee7\u7eed\u4e0a\u4e00\u7bc7\u7684\u8bdd\u9898\u4ecb\u7ecd\u5982\u4f55\u8ba1\u7b97<i>I<\/i><sub><i>n<\/i>\/1<\/sub>\u548c\u5176\u4f59\u7684LAOS\u53c2\u6570\u3002<\/p>\n<h3>LAOS\u5b9e\u9a8c\u662f\u600e\u4e48\u5b9e\u65bd\u7684<\/h3>\n<p>\u6211\u4eec\u662f\u5728TA ARES-RFS\u6d41\u53d8\u4eea\u4e0a\u505aLAOS\u5b9e\u9a8c\u3002\u516c\u53f8\u7684\u540d\u5b57\uff1a<a href=\"http:\/\/www.tainstruments.com\/\" target=\"_blank\" rel=\"noopener noreferrer\">TA Instruments<\/a>\u3002\u8fd9\u662f\u4e00\u53f0\u5e94\u53d8\u63a7\u5236\u578b\u6d41\u53d8\u4eea\uff08strain-controlled rheometer\uff09\uff0c\u76f8\u6bd4\u4e4b\u4e0b\u540c\u516c\u53f8\u7684AR-G2\u5219\u662f\u5e94\u529b\u63a7\u5236\u578b\uff08stress-controlled\uff09\u3002<a href=\"http:\/\/www.andrewsun.net\/panta_rhei\/wp-content\/uploads\/2013\/05\/AR-G2\u548cARES.pdf\">\u8fd9\u4e2a\u5c0f\u518c\u5b50<\/a>\u4e0a\u4ecb\u7ecd\u4e86ARES\u548cAR-G2\u4e24\u53f0\u6d41\u53d8\u4eea\u7684\u7279\u70b9\uff0c\u5176\u4e2d\u7684\u539f\u7406\u56fe\u548c\u5177\u4f53\u53c2\u6570\u53ef\u4ee5\u7528\u5728\u6bd5\u4e1a\u8bba\u6587\u4e2d\u3002\u8fdb\u884cLAOS\u5b9e\u9a8c\u9700\u8981\u6d41\u53d8\u4eea\u6301\u7eed\u5bf9\u6837\u54c1\u65bd\u52a0\u6b63\u5f26\u5e94\u53d8\uff0c\u6211\u4eec\u662f\u5229\u7528\u6d41\u53d8\u4eea\u63a7\u5236\u8f6f\u4ef6TA Orchestrator 7.2.1\u81ea\u5e26\u7684\u6d4b\u8bd5\u6a21\u5f0fdynamic time sweep\u6765\u63a7\u5236\u6d41\u53d8\u4eea\u8fdb\u884c\u8fd9\u4e00\u64cd\u4f5c\u3002Dynamic time sweep\u662f\u56fa\u5b9a\u632f\u8361\u7684\u5e94\u53d8\u5e45\u5ea6<i>\u03b3<\/i><sub>0<\/sub>\u548c\u9891\u7387<i>\u03c9<\/i>\uff0c\u6d4b\u91cf<i>G&#8217;<\/i>\u548c<i>G&#8221;<\/i>\u968f\u65f6\u95f4\u53d8\u5316\u7684\u6d4b\u8bd5\uff0c\u6240\u4ee5\u6b63\u9002\u5408\u6211\u4eec\u3002\u5728Orchestrator\u8f6f\u4ef6\u4e2d\u8bbe\u5b9a\u597ddynamic time sweep\u7684\u5e94\u53d8\u548c\u9891\u7387\uff0c\u4eea\u5668\u5c31\u4f1a\u4ee5\u76f8\u5e94\u7684\u6b63\u5f26\u51fd\u6570\u53bb\u63a7\u5236\u9a6c\u8fbe\u4e86\u3002\u6b64\u65f6\uff0c\u6211\u4eec\u9700\u8981\u9a6c\u4e0a\u4ece\u4eea\u5668\u80cc\u540e\u7684\u6a21\u62df\u8f93\u51fa\u7aef\u53e3\u540c\u65f6\u8bfb\u51fa\u4eea\u5668\u7684\u6d4b\u91cf\u4fe1\u53f7\uff0c\u5e76\u7528\u4e00\u4e2a\u6570\u6a21\u8f6c\u6362\u5668\uff08analog-to-digital converter, ADC\uff09\u8f6c\u6362\u6210\u6570\u5b57\u4fe1\u53f7\uff0c\u8f93\u5165\u5230\u8ba1\u7b97\u673a\u3002\u6211\u4eec\u7528\u7684ADC\u662f<a href=\"http:\/\/sine.ni.com\/nips\/cds\/view\/p\/lang\/zhs\/nid\/13881\" target=\"_blank\" rel=\"noopener noreferrer\">NI USB-9215A<\/a>\uff0c\u8981\u901a\u8fc7\u7535\u8111\u6765\u63a7\u5236\u5b83\u4f55\u65f6\u5f00\u59cb\u548c\u505c\u6b62\u91c7\u6837\uff0c\u4ee5\u53ca\u4ee5\u591a\u5927\u7684\u91c7\u6837\u9891\u7387\u8fdb\u884c\u91c7\u6837\u3002\u8bb8\u591a\u8f6f\u4ef6\u90fd\u53ef\u4ee5\u901a\u8fc7\u5b83\u7684\u9a71\u52a8\u7a0b\u5e8f\u63a5\u53e3\u6765\u5b9e\u65bd\u63a7\u5236\uff08MATLAB\u672c\u8eab\u5c31\u53ef\u4ee5\uff09\uff0c\u5728LAOS\u5b9e\u9a8c\u4e2d\u6211\u4eec\u7528\u4e00\u4e2aLabView\u5f00\u53d1\u7684\u5de5\u5177FT Meassurement\u6765\u91c7\u96c6\u6570\u636e\u3002\u56e0\u6b64\uff0c\u6211\u4eec\u7528\u4e00\u53f0\u7535\u8111\uff0c\u7528\u4e24\u4e2a\u8f6f\u4ef6\u5206\u800c\u63a7\u5236\u4e0d\u540c\u7684\u8fc7\u7a0b\u3002Orchestrator\u63a7\u5236\u6d41\u53d8\u4eea\u7684\u8fd0\u4f5c\uff0c\u800cFT Meassurement\u63a7\u5236ADC\u3002\u8fd9\u4e00\u6d41\u7a0b\u56fe\u53ef\u53c2\u8003<span id=\"cite_ITEM-5377-0\" name=\"citation\"><a href=\"#ITEM-5377-0\">[1]<\/a><\/span>\u548c<span id=\"cite_ITEM-5377-1\" name=\"citation\"><a href=\"#ITEM-5377-1\">[2]<\/a><\/span>\u4e2d\u7684\u7528\u56fe\u3002\u5177\u4f53\u4fe1\u53f7\u7ebf\u63a5\u6cd5\u548c\u5904\u7406\u65b9\u5f0f\u89c1\u4e0b\u9762\u7684PPT\uff08\u53ef\u4e0b\u8f7d\uff09\u3002<\/p>\n<div style=\"width:425px;text-align:left\"><a style=\"font:14px Helvetica,Arial,Sans-serif;color: #0000CC;display:block;margin:12px 0 3px 0;text-decoration:underline;\" href=\"\/\/www.slideboom.com\/presentations\/753593\/ARES%E6%A8%A1%E6%8B%9F%E8%BE%93%E5%87%BA\" title=\"ARES\u6a21\u62df\u8f93\u51fa\">ARES\u6a21\u62df\u8f93\u51fa<\/a><object classid=\"clsid:d27cdb6e-ae6d-11cf-96b8-444553540000\" codebase=\"http:\/\/fpdownload.macromedia.com\/pub\/shockwave\/cabs\/flash\/swflash.cab#version=9,0,28,0\" width=\"425\" height=\"370\" id=\"onlinePlayer753593\"><param name=\"movie\" value=\"\/\/www.slideboom.com\/player\/player.swf?id_resource=753593\"\/><param name=\"allowScriptAccess\" value=\"always\"\/><param name=\"quality\" value=\"high\"\/><param name=\"bgcolor\" value=\"#ffffff\"\/><param name=\"allowFullScreen\" value=\"true\"\/><param name=\"flashVars\" value=\"\"\/><\/object><\/p>\n<div style=\"font-size:11px;font-family:tahoma,arial;height:26px;padding-top:2px;\">View <a href=\"\" style=\"color: #0000CC;\">more presentations<\/a> or <a href=\"\/upload\" style=\"color: #0000CC;\">Upload<\/a> your own.<\/div>\n<\/div>\n<p>\u4e0a\u7bc7\u6587\u7ae0\u4e5f\u8bf4\u8fc7\uff0c\u4ece\u6d41\u53d8\u4eea\u91c7\u96c6\u5230\u7684\u4e00\u4e2a\u662f\u9a6c\u8fbe\u4f4d\u79fb\u7684\u7535\u538b\u4fe1\u53f7\uff0c\u53e6\u4e00\u4e2a\u662f\u529b\u77e9\u7684\u7535\u538b\u4fe1\u53f7\uff0c\u5b83\u4eec\u90fd\u8981\u4e58\u4ee5\u4e00\u4e2a\u7cfb\u6570\uff0c\u624d\u662f\u5e94\u53d8\u548c\u5e94\u529b\u3002\u4eceARES\u6d41\u53d8\u4eea\u7684\u8bf4\u4e66\u4e2d\u53ef\u4ee5\u67e5\u5230\u80cc\u677f\u8f93\u51fa\u4fe1\u53f7\u7684\u5177\u4f53\u60c5\u51b5\uff1a<\/p>\n<ul>\n<li>TORQUE OUT\uff1a\u4ece0\u5230\u6ee1\u91cf\u7a0b\uff0c\u5bf9\u5e94\u7535\u538b\u662f0 ~ 5 V\u3002\u7531\u4e8e\u8f6c\u77e9\u53ef\u4ee5\u6709\u4e24\u4e2a\u65b9\u5411\uff0c\u6240\u4ee5\u603b\u7684\u7535\u538b\u8303\u56f4\u5c31\u662f-5 ~ +5 V<\/li>\n<li>STRAIN OUT\uff1a\u867d\u7136\u6807\u8bb0\u662fSTRAIN\uff0c\u4f46\u5176\u5b9e\u53ea\u662f\u9a6c\u8fbe\u8f6c\u52a8\u7684\u89d2\u4f4d\u79fb\u3002\u4ece0 ~ 0.5 rad\u5bf9\u5e94\u7535\u538b\u662f0~5V\uff0c\u8003\u8651\u4e24\u4e2a\u8f6c\u52a8\u65b9\u5411\uff0c\u603b\u7535\u538b\u8303\u56f4\u662f-5~+5 V<\/li>\n<\/ul>\n<p>TORQUE OUT\u7684\u201c\u6ee1\u91cf\u7a0b\u201d\u5230\u5e95\u662f\u591a\u5c11\u5462\uff1f\u7531\u4e8e\u6211\u4eec\u7684ARES\u6709\u4e24\u4e2a\u6863\u4f4d\u7684\u529b\u77e9\u4f20\u611f\u5668\u3002Xducer 1\u7684\u4f20\u611f\u5668\u53eb\u505a\u201c20g FRT\u201d\u300220g\u662f\u6307\u8be5\u6863\u4f4d\u7684\u6700\u5927\u91cf\u7a0b\u662f20 g\u00b7cm\uff0c\u529b\u77e9\u7684\u4e00\u4e2a\u975eSI\u5355\u4f4d\uff0cSI\u5355\u4f4d\u662fN\u00b7m\u30021 g\u00b7cm = 98.066E-6 N\u00b7m\u3002\u53ef\u4ee5\u53bb<a href=\"http:\/\/www.unitconversion.org\/unit_converter\/torque.html\">\u6b64\u7f51\u7ad9<\/a>\u8fdb\u884c\u6362\u7b97\u3002FRT\u662fforce rebalance transducer\u7684\u7f29\u5199\uff0c\u8fd9\u662fARES\u7684\u4f20\u611f\u5668\u91c7\u7528\u7684\u4e00\u79cd\u6280\u672f\uff08<a href=\"https:\/\/www.google.com\/url?sa=t&amp;rct=j&amp;q=&amp;esrc=s&amp;source=web&amp;cd=1&amp;cad=rja&amp;ved=0CFYQFjAA&amp;url=http%3A%2F%2Fwww.tainstruments.com%2Flibrary_download.aspx%3Ffile%3DAPN008_FRT_Technology.pdf&amp;ei=0AiCUfLiJITiiALRuYAw&amp;usg=AFQjCNGiFMqn6IlCUX1mQXIMsidiv1YLmQ&amp;sig2=phvlSo98PDsDPKiFc9OQPQ&amp;bvm=bv.45960087,d.cGE\">\u53c2\u8003<\/a>\uff09\u3002\u6240\u4ee520g FRT\u7684\u6700\u5927\u91cf\u7a0b\u662f1.96E-3 N\u00b7m\u3002\u53e6\u4e00\u4e2a\u6863\u4f4dXducer2\u662f1k FRT\uff0c\u4e5f\u5c31\u662f\u6700\u5927\u91cf\u7a0b\u662f0.0981N\u00b7m\u3002\u56e0\u6b64\uff0c\u5230\u5e95TORQUE OUT\u8f93\u51fa\u7684\u7535\u538b\u503c\u5bf9\u5e94\u591a\u5927\u7684\u529b\u77e9\uff0c\u8981\u770b\u5f53\u65f6\u4eea\u5668\u5728\u7ebf\u7684\u4f20\u611f\u5668\u6863\u4f4d\u662fXducer1\u8fd8\u662fXducer2\u3002\u4ee5\u4e0b\u662f\u66f4\u8be6\u7ec6\u7684\u53c2\u6570\uff1a<\/p>\n<table class=\"tableizer-table\">\n<tbody>\n<tr class=\"tableizer-firstrow\">\n<td>Transducer<\/td>\n<td>1<\/td>\n<td>2<\/td>\n<\/tr>\n<tr>\n<td>Transducer Description<\/td>\n<td>20g FRT<\/td>\n<td>1k FRT<\/td>\n<\/tr>\n<tr>\n<td>Maximum Torque (g\u00b7cm)<\/td>\n<td>20<\/td>\n<td>1000<\/td>\n<\/tr>\n<tr>\n<td>Minimum Torque (g\u00b7cm)<\/td>\n<td>0.004<\/td>\n<td>1<\/td>\n<\/tr>\n<tr>\n<td>Torque Calibration Value<\/td>\n<td>21.34<\/td>\n<td>1050.7<\/td>\n<\/tr>\n<tr>\n<td>Torque Compliance<\/td>\n<td>6.67E-06<\/td>\n<td>6.67E-06<\/td>\n<\/tr>\n<tr>\n<td>Inertia Constant (g\u00b7cm^2)<\/td>\n<td>660<\/td>\n<td>660<\/td>\n<\/tr>\n<tr>\n<td>Phase Adjust Constant (rad\u00b7s\/rad)<\/td>\n<td>-5.80E-05<\/td>\n<td>-5.80E-05<\/td>\n<\/tr>\n<tr>\n<td>Maximum Normal Force (g)<\/td>\n<td>2000<\/td>\n<td>2000<\/td>\n<\/tr>\n<tr>\n<td>Minimum Normal Force (g)<\/td>\n<td>2.00E+00<\/td>\n<td>2.00E+00<\/td>\n<\/tr>\n<tr>\n<td>Normal Calibration Value<\/td>\n<td>2101.8<\/td>\n<td>2101.8<\/td>\n<\/tr>\n<tr>\n<td>Normal Compliance (um\/kg)<\/td>\n<td>0.00E+00<\/td>\n<td>0.00E+00<\/td>\n<\/tr>\n<tr>\n<td>Phase Offset (rad)<\/td>\n<td>0<\/td>\n<td>0<\/td>\n<\/tr>\n<tr>\n<td>Motor Temp Reference (\u00b0C)<\/td>\n<td colspan=\"2\">3.27E+01<\/td>\n<\/tr>\n<tr>\n<td>Motor Temp Gain<\/td>\n<td colspan=\"2\">2.9445<\/td>\n<\/tr>\n<tr>\n<td>Compliance Gain<\/td>\n<td colspan=\"2\">7.89E-01<\/td>\n<\/tr>\n<\/tbody>\n<\/table>\n<p>\u8bb0STRAIN OUT\u8f93\u51fa\u7535\u538b\u4e3a<i>V<\/i><sub>s<\/sub>\uff0cTORQUE OUT\u8f93\u51fa\u7535\u538b\u4e3a<i>V<\/i><sub>t<\/sub>\uff0c\u6362\u7b97\u6210\u76f8\u5e94\u7684\u89d2\u4f4d\u79fb<i>\u03b8<\/i>\u8f6c\u77e9<i>M<\/i>\u7684\u516c\u5f0f\u662f\uff1a<img decoding=\"async\" src=\"https:\/\/s0.wp.com\/latex.php?latex=%5Ctheta%3Dk_%5Ctext%7Bs%7DV_%5Ctext%7Bs%7D&#038;bg=ffffff&#038;fg=000&#038;s=0&#038;c=20201002\" alt=\"&#92;theta=k_&#92;text{s}V_&#92;text{s}\" class=\"latex\" \/>\u3001<img decoding=\"async\" src=\"https:\/\/s0.wp.com\/latex.php?latex=M%3Dk_%7B%5Ctext%7Bt%7D%2Ci%7DV_%5Ctext%7Bt%7D&#038;bg=ffffff&#038;fg=000&#038;s=0&#038;c=20201002\" alt=\"M=k_{&#92;text{t},i}V_&#92;text{t}\" class=\"latex\" \/>\uff0c\u5176\u4e2d\uff0c\u8f6c\u6362\u7cfb\u6570<i>k<\/i><sub>t<\/sub> = 0.1 rad\/V\uff0c<i>k<\/i><sub>t,1<\/sub> = 3.92E-4 N\u00b7m\/V\uff0c<i>k<\/i><sub>t,2<\/sub> = 0.0196 N\u00b7m\/V\u3002\u4ece\u89d2\u4f4d\u79fb\uff08rad\uff09\u5230\u5e94\u53d8\uff08\u91cf\u7eb2\u4e00\u91cf\uff09\uff0c\u4ee5\u53ca\u4ece\u8f6c\u77e9\uff08N\u00b7m\uff09\u5230\u5e94\u529b\uff08Pa\uff09\uff0c\u8fd8\u5404\u9700\u8981\u4e58\u4e00\u4e2a\u7cfb\u6570<i>F<\/i><sub>\u03b3<\/sub>\u548c<i>F<\/i><sub>\u03c3<\/sub>\uff0c\u8fd9\u4e2a\u7cfb\u6570\u8ddf\u6240\u9009\u7528\u7684\u5939\u5177\u79cd\u7c7b\u548c\u5c3a\u5bf8\u6709\u5173\u3002\u6d41\u53d8\u4eea\u7684\u8bf4\u660e\u4e66\u4f1a\u4ecb\u7ecd\u5404\u79cd\u5939\u5177\u7684\u7cfb\u6570\u5982\u4f55\u4ece\u5939\u5177\u7684\u5c3a\u5bf8\u6765\u6362\u7b97\u3002\u8fd9\u91cc\u53ea\u4e3e\u9525\u677f\u5939\u5177\u7684\u4f8b\u5b50\uff1a<\/p>\n<div id=\"attachment_5391\" style=\"width: 636px\" class=\"wp-caption alignnone\"><a href=\"http:\/\/www.andrewsun.net\/panta_rhei\/wp-content\/uploads\/2013\/05\/cap3.png\"><img loading=\"lazy\" decoding=\"async\" aria-describedby=\"caption-attachment-5391\" data-attachment-id=\"5391\" data-permalink=\"https:\/\/www.andrewsun.net\/panta_rhei\/archives\/5377\/cap3\" data-orig-file=\"https:\/\/www.andrewsun.net\/panta_rhei\/wp-content\/uploads\/2013\/05\/cap3.png\" data-orig-size=\"626,463\" data-comments-opened=\"0\" data-image-meta=\"{&quot;aperture&quot;:&quot;0&quot;,&quot;credit&quot;:&quot;&quot;,&quot;camera&quot;:&quot;&quot;,&quot;caption&quot;:&quot;&quot;,&quot;created_timestamp&quot;:&quot;0&quot;,&quot;copyright&quot;:&quot;&quot;,&quot;focal_length&quot;:&quot;0&quot;,&quot;iso&quot;:&quot;0&quot;,&quot;shutter_speed&quot;:&quot;0&quot;,&quot;title&quot;:&quot;&quot;}\" data-image-title=\"cone-plate\" data-image-description=\"\" data-image-caption=\"&lt;p&gt;Figure 1 Cone-plate geometry&lt;\/p&gt;\n\" data-large-file=\"https:\/\/www.andrewsun.net\/panta_rhei\/wp-content\/uploads\/2013\/05\/cap3.png\" src=\"http:\/\/www.andrewsun.net\/panta_rhei\/wp-content\/uploads\/2013\/05\/cap3.png\" alt=\"Figure 1 Cone-plate geometry\" width=\"626\" height=\"463\" class=\"size-full wp-image-5391\" srcset=\"https:\/\/www.andrewsun.net\/panta_rhei\/wp-content\/uploads\/2013\/05\/cap3.png 626w, https:\/\/www.andrewsun.net\/panta_rhei\/wp-content\/uploads\/2013\/05\/cap3-480x355.png 480w\" sizes=\"auto, (max-width: 626px) 100vw, 626px\" \/><\/a><p id=\"caption-attachment-5391\" class=\"wp-caption-text\">Figure 1 Cone-plate geometry<\/p><\/div>\n<p>$$F_\\gamma=\\frac{1}{\\tan\\alpha},\\quad F_\\sigma=\\frac{3}{2\\pi R^3}$$\u6240\u4ee5\uff0c\u6700\u7ec8\u7684\u5e94\u53d8\u548c\u5e94\u529b\u5e94\u8be5\u662f$$\\gamma=F_\\gamma k_\\text{s}V_\\text{s},\\quad\\sigma=F_\\sigma k_{\\text{s},i}V_\\text{t}$$<\/p>\n<h3>\u5b9e\u9a8c\u6570\u636e\u5904\u7406<\/h3>\n<p>\u4ece\u4eea\u5668\u80cc\u677fTORQUE OUT\u548cSTRAIN OUT\u8fde\u7ebf\u5230ADC\u7684channel 1\u548cchannel 2\u8f93\u5165\uff0c\u7136\u540e\u5728\u8ba1\u7b97\u673a\u4e2d\u7684FT Measurement\u63a7\u5236ADC\u4ee5\u4e00\u5b9a\u7684\u91c7\u6837\u9891\u7387<i>f<\/i><sub>s<\/sub>\u8fdb\u884c\u91c7\u6837\uff0c\u5c31\u4f1a\u751f\u6210\u4e00\u4e2a\u6587\u672c\u6570\u636e\u6587\u4ef6\uff0c\u6b64\u4f8b\u7684\u6587\u4ef6\u540d\u662f\u201cDTimeSwp (13) 000 .txt\u201d\u3002\u7b2c\u4e00\u884c\u662f\u4e00\u4e9b\u8bf4\u660e\u6027\u7684\u6570\u5b57\uff0c\u7136\u540e\u5c31\u662f\u4e24\u5217\u6570\u636e\uff0c\u5206\u522b\u5bf9\u5e94\u7740channel 1\u548cchannel 2\u7684\u7535\u538b\u6d4b\u91cf\u503c\uff0c\u6309\u7167\u901a\u5e38\u7684\u63a5\u7ebf\u65b9\u5f0f\uff0c\u7b2c\u4e00\u5217\u662fSTRAIN OUT\u4fe1\u53f7\uff0c\u7b2c\u4e8c\u5217\u662fTORQUE OUT\u3002\u5728MATALB\u4e2d\u9884\u89c8\u51fa\u4e0b\uff1a<\/p>\n<div id=\"attachment_5401\" style=\"width: 712px\" class=\"wp-caption alignnone\"><a href=\"http:\/\/www.andrewsun.net\/panta_rhei\/wp-content\/uploads\/2013\/05\/cap.png\"><img loading=\"lazy\" decoding=\"async\" aria-describedby=\"caption-attachment-5401\" data-attachment-id=\"5401\" data-permalink=\"https:\/\/www.andrewsun.net\/panta_rhei\/archives\/5377\/cap\" data-orig-file=\"https:\/\/www.andrewsun.net\/panta_rhei\/wp-content\/uploads\/2013\/05\/cap.png\" data-orig-size=\"702,435\" data-comments-opened=\"0\" data-image-meta=\"{&quot;aperture&quot;:&quot;0&quot;,&quot;credit&quot;:&quot;&quot;,&quot;camera&quot;:&quot;&quot;,&quot;caption&quot;:&quot;&quot;,&quot;created_timestamp&quot;:&quot;0&quot;,&quot;copyright&quot;:&quot;&quot;,&quot;focal_length&quot;:&quot;0&quot;,&quot;iso&quot;:&quot;0&quot;,&quot;shutter_speed&quot;:&quot;0&quot;,&quot;title&quot;:&quot;&quot;}\" data-image-title=\"fig2\" data-image-description=\"\" data-image-caption=\"&lt;p&gt;Figure 2 Data file from FT Measurement&lt;\/p&gt;\n\" data-large-file=\"https:\/\/www.andrewsun.net\/panta_rhei\/wp-content\/uploads\/2013\/05\/cap.png\" src=\"http:\/\/www.andrewsun.net\/panta_rhei\/wp-content\/uploads\/2013\/05\/cap.png\" alt=\"Figure 2 Data file from FT Measurement\" width=\"702\" height=\"435\" class=\"size-full wp-image-5401\" srcset=\"https:\/\/www.andrewsun.net\/panta_rhei\/wp-content\/uploads\/2013\/05\/cap.png 702w, https:\/\/www.andrewsun.net\/panta_rhei\/wp-content\/uploads\/2013\/05\/cap-480x297.png 480w\" sizes=\"auto, (max-width: 702px) 100vw, 702px\" \/><\/a><p id=\"caption-attachment-5401\" class=\"wp-caption-text\">Figure 2 Data file from FT Measurement<\/p><\/div>\n<p>\u7528importdata\u547d\u4ee4\u53ef\u4ee5\u81ea\u52a8\u5904\u7406\u5177\u6709\u8868\u5934\u7684\u6570\u636e\u6587\u4ef6\uff0c\u628a\u8868\u5934\u6587\u5b57\u548c\u6570\u636e\u5206\u5f00\u3002<\/p>\n<p><code lang=\"matlab\"><br \/>\nclear all<br \/>\nclc<\/code><\/p>\n<p><code lang=\"matlab\"><br \/>\n<\/code><code lang=\"matlab\">A=importdata('DTimeSwp (13) 000 .txt')<br \/>\n<\/code><\/p>\n<p>\u89c2\u5bdfA\u7684\u8fd4\u56de\u4fe1\u606f\u3002\u5982\u679c\u6e90\u6587\u4ef6\u6ca1\u6709\u8868\u5934\uff0c\u662f\u7eaf\u6570\u636e\uff0cA\u5c31\u662f\u76f4\u63a5\u7531\u8fd9\u4e9b\u6570\u636e\u7ec4\u6210\u7684\u77e9\u9635\uff1b\u5982\u679c\u6709\u8868\u5934\uff0cA\u5c31\u662f\u4e00\u4e2astruct\u7c7b\u578b\uff0c\u5305\u542b\u4e00\u4e2adata\u5355\u5143\u548c\u4e00\u4e2atextdata\u5355\u5143\u3002textdata\u662f\u4ee5\u8868\u5934\u4e3a\u5185\u5bb9\u7684\u5b57\u7b26\u4e32\uff0cdata\u5355\u5143\u5c31\u662f\u6570\u636e\u7ec4\u6210\u7684\u77e9\u9635\u3002\u8981\u8c03\u7528data\uff0c\u8bed\u6cd5\u662fA.data\u3002\u4e3a\u4e86\u7b80\u5355\uff0c\u5c31\u628a\u6570\u636e\u91cd\u65b0\u653e\u5728\u4e00\u4e2a\u65b0\u7684\u53d8\u91cf\u4e2d\uff1a<\/p>\n<p><code lang=\"matlab\"><br \/>\nx=A.data;<br \/>\n<\/code><\/p>\n<p>DTimeSwp (13) 000 .txt\u8fd9\u4e2a\u6587\u4ef6\uff0c\u5bf9\u5e94\u7684\u662f\u4e00\u4e2adynamic time sweep\u6d4b\u8bd5\uff0c\u547d\u4ee4\u7684\u5e94\u53d8\u5e45\u5ea6<i>\u03b3<\/i><sub>0<\/sub> = 160%\uff0c\u89d2\u9891\u7387\u662f<i>\u03c9<\/i> = 6.283 rad\/s\uff08<i>f<\/i> = 1.0 Hz\uff09\u3002FT Measurement\u63a7\u5236ADC\u4ee5<i>f<\/i><sub>s<\/sub> = 200 Hz\u7684\u91c7\u6837\u9891\u7387\u8fdb\u884c\u91c7\u6837\u3002\u6211\u4eec\u53ef\u4ee5\u4ece<i>f<\/i><sub>s<\/sub>\u91cd\u6784\u4e00\u5217\u65f6\u95f4\u6570\u636e\uff0c\u62fc\u5230\u53d8\u91cfx\u4e2d\uff1a<\/p>\n<p><code lang=\"matlab\"><br \/>\nfs=200; % the sampling frequency was fixed by the test condition<\/code><\/p>\n<p><code lang=\"matlab\">t=0:1\/fs:(length(x)-1)\/fs; % construct the time series<br \/>\nt=t(:);<\/p>\n<p><\/code><code lang=\"matlab\">x=[t x]; % combine the time series and the signals<br \/>\n<\/code><\/p>\n<p>\u8fd9\u6837\uff0c\u53d8\u91cfx\u7b2c\u4e00\u5217\u662f\u65f6\u95f4\uff0c\u7b2c2\u30013\u5217\u624d\u5206\u522b\u662fSTRAIN OUT\u548cTORQUE OUT\u7535\u538b\u4fe1\u53f7\u3002\u8fd9\u4e2a\u5b9e\u9a8c\u662f\u7528\u4e00\u4e2a\u9525\u677f\u5939\u5177\u6765\u505a\u7684\uff0c\u76f4\u5f8450 mm\uff0c\u9525\u5ea60.04 rad\u3002\u6d4b\u8bd5\u65f6\uff0c\u5728\u7ebf\u4f20\u611f\u5668\u662fxducer 1\u3002\u56e0\u6b64\u6839\u636e\u8ba1\u7b97\u516c\u5f0f\uff0c<i>F<\/i><sub>\u03b3<\/sub> = 24.99\uff0c<i>F<\/i><sub>\u03c3<\/sub> = 30557.75\uff0c<i>k<\/i><sub>s<\/sub>\u548c<i>k<\/i><sub>t,1<\/sub>\u7684\u503c\u524d\u6587\u5df2\u7ecf\u8fc7\u4e86\u3002\u628ax\u53d8\u91cf\u7684\u6570\u636e\u8f6c\u6362\u6210\u5e94\u529b\u548c\u5e94\u53d8\uff1a<\/p>\n<p><code lang=\"matlab\"><br \/>\n% set all the coefficients<br \/>\nF_gamma=24.99;<br \/>\nF_sigma=30557.75;<br \/>\nks=0.1;<br \/>\nkt1=3.92e-4;<\/code><\/p>\n<p><code lang=\"matlab\"><br \/>\n<\/code><code lang=\"matlab\">% convert voltage to strain\/stress<br \/>\nx(:,2)=F_gamma<em>ks.<\/em>x(:,2);<br \/>\nx(:,3)=F_sigma<em>kt1.<\/em>x(:,3);<br \/>\n<\/code><\/p>\n<h3>\u83b7\u53d6\u4fe1\u53f7\u7684\u9891\u7387<\/h3>\n<p>\u81f3\u6b64\uff0c\u5bf9\u53d8\u91cfx\u7684\u6ce2\u5f62\u91cd\u6784\u53ef\u4ee5\u5b8c\u5168\u8ddf\u4e4b\u524d\u6587\u7ae0\u4ecb\u7ecd\u7684\u4e00\u6837\u7684\uff0c\u4e0d\u518d\u91cd\u590d\u3002\u4f46\u662f\u672c\u6587\u518d\u4f5c\u4e00\u9879\u6539\u8fdb\u3002\u524d\u9762\u51e0\u7bc7\u6587\u7ae0\u8bf4\u8fc7\uff0c\u5b9e\u9645\u5e94\u53d8\u503c\u8ddf\u8f6f\u4ef6\u8bbe\u5b9a\u7684\u547d\u4ee4\u6709\u53ef\u80fd\u6709\u6240\u504f\u5dee\uff0c\u52a0\u4e0a\u4eea\u5668\u566a\u97f3\u7684\u5f71\u54cd\uff0c\u6240\u4ee5\u6211\u4eec\u8981\u91cd\u6784\u5e94\u53d8\u7684\u4fe1\u53f7\u6765\u51c6\u786e\u83b7\u5f97\u5b9e\u9645\u7684\u5e94\u53d8\u5e45\u5ea6\u548c\u9891\u7387\u3002\u800c\u51c6\u786e\u7684FFT\u7ed3\u679c\u8981\u6c42\u5f85\u505aFFT\u7684\u4fe1\u53f7\u662f\u201c\u76f8\u5e72\u53d6\u6837\u201d\u7684\u3002\u505a\u76f8\u5e72\u53d6\u6837\u53c8\u8981\u6c42\u6211\u4eec\u81f3\u5c11\u8981\u51c6\u786e\u77e5\u9053\u4fe1\u53f7\u7684\u9891\u7387\u3002\u89e3\u51b3\u8fd9\u4e00\u77db\u76fe\u7684\u65b9\u6cd5\u662f\uff0c\u5229\u7528\u5e94\u53d8\u5fc5\u7136\u662f\u6b63\u5f26\u6ce2\u7684\u6027\u8d28\uff0c\u5148\u901a\u8fc7\u6b63\u5f26\u51fd\u6570\u62df\u5408\u6765\u83b7\u53d6\u4fe1\u53f7\u7684\u5e94\u53d8\u548c\u9891\u7387\u3002\u4e8b\u5b9e\u4e0a\uff0c\u5bf9\u4e8e\u4e00\u4e2a\u6b63\u5f26\u6ce2\uff0c\u6b63\u5f26\u62df\u5408\u548cFFT\u90fd\u662f\u91cd\u6784\u7684\u65b9\u6cd5\uff0c\u4f46\u5b9e\u9645\u4e0a\u6b63\u5f26\u62df\u5408\u7684\u5e45\u5ea6\u548c\u76f8\u4f4d\u5f80\u5f80\u4e0d\u51c6\uff0c\u6240\u4ee5\u53ea\u8981\u80fd\u505a\u597d\u76f8\u5e72\u53d6\u6837\uff0c\u6211\u4eec\u90fd\u504f\u7231\u7528FFT\u505a\u91cd\u6784\uff1b\u4f46\u662f\u6b63\u5f26\u62df\u5408\u5f97\u5230\u7684\u9891\u7387\u662f\u51c6\u7684\uff0c\u800c\u8fd9\u65f6\u6211\u4eec\u53ea\u9700\u8981\u77e5\u9053\u4e00\u4e2a\u9891\u7387\uff0c\u56e0\u6b64\u53ef\u4ee5\u91c7\u7528\u6b63\u5f26\u62df\u5408\u6765\u5b8c\u6210\u3002<\/p>\n<p>\u6211\u4eec\u8c03\u7528\u4e00\u4e2a\u522b\u4eba\u5f00\u53d1\u7684\u4ee3\u7801\u8fdb\u884c\uff1a<a href=\"http:\/\/www.mathworks.com\/matlabcentral\/fileexchange\/19902-frequency-amplitude-phase-and-mean-value-of-sine-wave\">sinfapm<\/a>\u3002\u5176\u8bed\u6cd5\u5728\u4ee3\u7801\u5f00\u5934\u7684\u6ce8\u91ca\u6587\u4ef6\u4e2d\u6709\u6e05\u695a\u7684\u4ecb\u7ecd\u3002\u6ce8\u610f\uff0csinfapm\u4ee3\u7801\u53c8\u8c03\u7528\u4e86\u53e6\u4e00\u4e2a\u7528\u4e8e\u8fdb\u884c\u975e\u7ebf\u6027\u6700\u5c0f\u5e73\u65b9\u6c42\u89e3\u7684\u7b2c\u4e09\u65b9\u4ee3\u7801\uff1a<a href=\"http:\/\/www.mathworks.com\/matlabcentral\/fileexchange\/17534-lmfnlsq-solution-of-nonlinear-least-squares\">LMFnlsq<\/a>\uff0c\u9700\u8981\u90fd\u653e\u5728\u540c\u4e00\u4e2a\u6587\u4ef6\u5939\u3002<\/p>\n<p>sinfapm\u51fd\u6570\u8fd8\u6709\u4e00\u4e2a\u9ebb\u70e6\u4e4b\u5904\uff0c\u5c31\u662f\u5904\u7406\u53d6\u6837\u9891\u7387\u592a\u9ad8\u7684\u6570\u636e\u4f1a\u5931\u6548\u3002\u6240\u4ee5\uff0c\u5728\u4f7f\u7528\u524d\u8981\u4e34\u65f6\u5bf9\u4e00\u4e2a\u672a\u77e5\u4fe1\u53f7\u201c\u964d\u91c7\u6837\u201d\uff08down sampling\uff09\u3002\u7ecf\u9a8c\u8868\u660e\uff0c\u5bf9\u6bcf\u4e2a\u5468\u671f\u4e0d\u8d85\u8fc71000\u4e2a\u6570\u636e\u70b9\u7684\u6570\u636e\uff0csinfapm\u80fd\u591f\u7a33\u5b9a\u8868\u73b0\u3002\u56e0\u6b64\u5c31\u662f\u5728\u4f7f\u7528sinfapm\u524d\u8981\u52a0\u4e00\u6bb5\u4ee3\u7801\uff0c\u5982\u679c\u4fe1\u53f7\u6bcf\u5468\u671f\u8d85\u8fc71000\u4e2a\u70b9\uff0c\u5c31\u964d\u91c7\u6837\u4e3a\u6bcf\u5468\u671f1000\u4e2a\u70b9\uff1b\u5426\u5219\u5c31\u4e0d\u53d8\u3002\u9ebb\u70e6\u7684\u662f\uff0c\u4e3a\u4e86\u77e5\u9053\u539f\u4fe1\u53f7\u6bcf\u5468\u671f\u6709\u591a\u5c11\u4e2a\u70b9\uff0c\u6211\u4eec\u8fd8\u662f\u8981\u5148\u77e5\u9053\u4fe1\u53f7\u7684\u9891\u7387\u3002\u6240\u5e78\uff0c\u8fd9\u4e00\u6b65\u53ea\u9700\u8981\u7c97\u7565\u4f30\u7b97\u5373\u53ef\uff0c\u56e0\u6b64\uff0c\u505a\u4e00\u4e2a\u4e0d\u9760\u8c31\uff08\u6ca1\u6709\u76f8\u5e72\u91c7\u6837\uff09\u7684FFT\u7c97\u4f30\u4e00\u4e0b\u9891\u7387\u5c31\u884c\u4e86\u3002\u603b\u4e4b\uff0c\u6574\u4e2a\u7cbe\u786e\u83b7\u5f97\u9891\u7387\u7684\u6b65\u9aa4\u5c31\u662f\uff1a<\/p>\n<ol>\n<li>\u7528FFT\u7c97\u4f30\u9891\u7387<\/li>\n<li>\u6839\u636e\u7c97\u4f30\u9891\u7387\u8ba1\u7b97\u4fe1\u53f7\u6bcf\u5468\u671f\u6709\u591a\u5c11\u4e2a\u6570\u636e\u70b9\uff0c\u51b3\u5b9a\u964d\u53d6\u6837\u6bd4\u503c<\/li>\n<li>\u5bf9\u964d\u53d6\u6837\u7684\u6570\u636e\u8fdb\u884c\u6b63\u5f26\u62df\u5408\u5f97\u5230\u7cbe\u786e\u7684\u9891\u7387<\/li>\n<\/ol>\n<p>\u4ee5\u4e0b\u662f\u4ee3\u7801\uff1a<\/p>\n<p><code lang=\"matlab\"><br \/>\n% Roughly estimate the input frequency by FFT<br \/>\nN=length(x);<br \/>\nXraw=fft(x(:,2)); % needless to renormalized the amplitude coz we only want the frequency<\/code><\/p>\n<p><code lang=\"matlab\">% find the maximum peak and obtain the corresponding row index<br \/>\n% the first data is the DC component which is omitted because the value may<br \/>\n% be higher than the first harmonic and violate the peak finding<br \/>\n[I, J]=max(abs(Xraw(2:end)));<br \/>\n% I is useless<\/p>\n<p>% estimate the points per cycle of the signal<br \/>\npts_per_cycle=N\/J;<\/p>\n<p>if pts_per_cycle &gt; 1000<br \/>\n% select 1 out of every jump data to reach 1000 points per cycle<br \/>\njump = floor(pts_per_cycle\/1000);<br \/>\nelse<br \/>\njump=1;<br \/>\nend<\/p>\n<p>[f, amp, phi]=sinfapm(x(1:jump:end,2),fs\/jump);<br \/>\n% amp and phi are useless<\/p>\n<p><\/code><code lang=\"matlab\">f<br \/>\n<\/code><\/p>\n<p>\u6211\u4eec\u53ef\u4ee5\u4f5c\u56fe\u9a8c\u8bc1sinfapm\u662f\u5426\u6b63\u5e38\u5de5\u4f5c\u4e86\uff1a<\/p>\n<p><code lang=\"matlab\"><br \/>\nplot(t,amp<em>sin(2<\/em>pi<em>f<\/em>t+phi),'r-',t,x(:,2),'bo') % Figure 3<br \/>\n<\/code><\/p>\n<div id=\"attachment_5403\" style=\"width: 472px\" class=\"wp-caption alignnone\"><a href=\"http:\/\/www.andrewsun.net\/panta_rhei\/wp-content\/uploads\/2013\/05\/fig3.png\"><img loading=\"lazy\" decoding=\"async\" aria-describedby=\"caption-attachment-5403\" data-attachment-id=\"5403\" data-permalink=\"https:\/\/www.andrewsun.net\/panta_rhei\/archives\/5377\/fig3-2\" data-orig-file=\"https:\/\/www.andrewsun.net\/panta_rhei\/wp-content\/uploads\/2013\/05\/fig3.png\" data-orig-size=\"462,362\" data-comments-opened=\"0\" data-image-meta=\"{&quot;aperture&quot;:&quot;0&quot;,&quot;credit&quot;:&quot;&quot;,&quot;camera&quot;:&quot;&quot;,&quot;caption&quot;:&quot;&quot;,&quot;created_timestamp&quot;:&quot;0&quot;,&quot;copyright&quot;:&quot;&quot;,&quot;focal_length&quot;:&quot;0&quot;,&quot;iso&quot;:&quot;0&quot;,&quot;shutter_speed&quot;:&quot;0&quot;,&quot;title&quot;:&quot;&quot;}\" data-image-title=\"fig\" data-image-description=\"\" data-image-caption=\"&lt;p&gt;Figure 3 Effect of sinfapm&lt;\/p&gt;\n\" data-large-file=\"https:\/\/www.andrewsun.net\/panta_rhei\/wp-content\/uploads\/2013\/05\/fig3.png\" src=\"http:\/\/www.andrewsun.net\/panta_rhei\/wp-content\/uploads\/2013\/05\/fig3.png\" alt=\"Figure 3 Effect of sinfapm\" width=\"462\" height=\"362\" class=\"size-full wp-image-5403\"\/><\/a><p id=\"caption-attachment-5403\" class=\"wp-caption-text\">Figure 3 Effect of sinfapm<\/p><\/div>\n<p>\u8fde\u5e45\u5ea6\u548c\u76f8\u4f4d\u90fd\u62df\u5408\u5f97\u8fd9\u4e48\u597d\uff0c\u9891\u7387\u7684\u62df\u5408\u7ed3\u679c\u5e94\u8be5\u662f\u53ef\u4fe1\u7684\u4e86\u3002\u9891\u7387\u77e5\u9053\u4e86\u4e4b\u540e\uff0c\u5269\u4e0b\u7684\u4e8b\u60c5\u5c31\u4e0d\u65b0\u9c9c\u4e86\uff0c\u53c2\u89c1\u524d\u4e00\u7bc7\u6587\u7ae0\u3002<\/p>\n<p><code lang=\"matlab\"><br \/>\nN=length(x);<br \/>\npts_per_cycle=fs\/f;<br \/>\nN_cycle=floor(N\/pts_per_cycle);<\/code><\/p>\n<p><code lang=\"matlab\">N_cut=round(round(N_cycle\/3)*pts_per_cycle); % use the last third of cycles<br \/>\nx=x(length(x)-N_cut:end,:); % crop the last N_cut data<\/p>\n<p>Xraw=2*fft(x(:,2))\/N_cut;<br \/>\nXraw=Xraw(1:ceil(N_cut\/2));<br \/>\nfreq=0:fs\/N_cut:fs\/2-fs\/N_cut;<\/p>\n<p>A=abs(Xraw(round(N_cut<em>f\/fs)+1));<br \/>\ndelta0=wrapTo2Pi(angle(Xraw(round(N_cut<\/em>f\/fs)+1))+0.5<em>pi);<br \/>\nfrq=freq(round(N_cut<\/em>f\/fs)+1); % this line can be omitted and use the f instead<br \/>\nx_rec=A.<em>sin(2<\/em>pi<em>frq.<\/em>x(:,1)+delta0); % frp can be replaced by f<\/p>\n<p>Yraw=2*fft(x(:,3))\/N_cut;<br \/>\nYraw=Yraw(1:ceil(N_cut\/2));<\/p>\n<p>max_nr_harm=floor(fs\/(2*f));<br \/>\nif max_nr_harm\/2==floor(max_nr_harm\/2)<br \/>\nmax_nr_harm=max_nr_harm-1;<br \/>\nend<\/p>\n<p>max_nr_harm=max_nr_harm-2;<\/p>\n<p>if max_nr_harm&gt;25<br \/>\nmax_nr_harm=25;<br \/>\nend<\/p>\n<p>I_n=zeros((max_nr_harm+1)\/2,1);<br \/>\ndelta_n=zeros((max_nr_harm+1)\/2,1);<\/p>\n<p>for i=1:(max_nr_harm+1)\/2<br \/>\nI_n(i)=abs(Yraw(round((2<em>i-1)<\/em>N_cut<em>f\/fs)+1));<br \/>\ndelta_n(i)=angle(Yraw(round((2<\/em>i-1)<em>N_cut<\/em>f\/fs)+1))+0.5<em>pi;<br \/>\nend<br \/>\nDC=abs(Yraw(1))<\/em>cos(angle(Yraw(1)))\/2;<\/p>\n<p>y_rec=zeros(length(x(:,3)),1); % create the variables for the reconstructed signals<br \/>\nfor i=1:2:max_nr_harm<br \/>\ny_rec=y_rec+I_n((i+1)\/2).<em>sin(i<\/em>2<em>pi<\/em>f.*x(:,1)+delta_n((i+1)\/2));<br \/>\nend<br \/>\ny_rec=y_rec+DC;<\/p>\n<p><\/code><code lang=\"matlab\">plot(x(:,2),x(:,3),'b-',x_rec,y_rec,'r-') % Figure 4<br \/>\n<\/code><\/p>\n<p>\u770b\u6548\u679c\uff1a<\/p>\n<div id=\"attachment_5405\" style=\"width: 470px\" class=\"wp-caption alignnone\"><a href=\"http:\/\/www.andrewsun.net\/panta_rhei\/wp-content\/uploads\/2013\/05\/fig4.png\"><img loading=\"lazy\" decoding=\"async\" aria-describedby=\"caption-attachment-5405\" data-attachment-id=\"5405\" data-permalink=\"https:\/\/www.andrewsun.net\/panta_rhei\/archives\/5377\/fig4-2\" data-orig-file=\"https:\/\/www.andrewsun.net\/panta_rhei\/wp-content\/uploads\/2013\/05\/fig4.png\" data-orig-size=\"460,363\" data-comments-opened=\"0\" data-image-meta=\"{&quot;aperture&quot;:&quot;0&quot;,&quot;credit&quot;:&quot;&quot;,&quot;camera&quot;:&quot;&quot;,&quot;caption&quot;:&quot;&quot;,&quot;created_timestamp&quot;:&quot;0&quot;,&quot;copyright&quot;:&quot;&quot;,&quot;focal_length&quot;:&quot;0&quot;,&quot;iso&quot;:&quot;0&quot;,&quot;shutter_speed&quot;:&quot;0&quot;,&quot;title&quot;:&quot;&quot;}\" data-image-title=\"fig4\" data-image-description=\"\" data-image-caption=\"&lt;p&gt;Figure 4 Reconstruction of the LAOS results.&lt;\/p&gt;\n\" data-large-file=\"https:\/\/www.andrewsun.net\/panta_rhei\/wp-content\/uploads\/2013\/05\/fig4.png\" src=\"http:\/\/www.andrewsun.net\/panta_rhei\/wp-content\/uploads\/2013\/05\/fig4.png\" alt=\"Figure 4 Reconstruction of the LAOS results.\" width=\"460\" height=\"363\" class=\"size-full wp-image-5405\"\/><\/a><p id=\"caption-attachment-5405\" class=\"wp-caption-text\">Figure 4 Reconstruction of the LAOS results.<\/p><\/div>\n<p>\u6211\u4eec\u7684\u4fe1\u53f7\u662f\u5df2\u7ecf\u8f6c\u6362\u6210\u5e94\u529b\u548c\u5e94\u53d8\u7684\u4e86\u3002\u56e0\u6b64\uff0cFigure 4\u4e2d\u6a2a\u8f74\u662f\u5e94\u53d8\uff0c\u6b63\u8d1f\u6700\u503c\u90fd\u662f1.6\uff0c\u4e0e\u8f6f\u4ef6\u547d\u4ee4\u503c\uff08160%\uff09\u76f8\u7b26\u3002\u6211\u4eec\u6362\u4e00\u4e2a\u5e94\u53d8\u5e45\u5ea6\u4e3a250%\u5b9e\u9a8c\u6570\u636e\uff0c\u7ed3\u679c\u5982\u4e0b\uff1a<\/p>\n<div id=\"attachment_5411\" style=\"width: 475px\" class=\"wp-caption alignnone\"><a href=\"http:\/\/www.andrewsun.net\/panta_rhei\/wp-content\/uploads\/2013\/05\/fig41.png\"><img loading=\"lazy\" decoding=\"async\" aria-describedby=\"caption-attachment-5411\" data-attachment-id=\"5411\" data-permalink=\"https:\/\/www.andrewsun.net\/panta_rhei\/archives\/5377\/fig4-3\" data-orig-file=\"https:\/\/www.andrewsun.net\/panta_rhei\/wp-content\/uploads\/2013\/05\/fig41.png\" data-orig-size=\"465,363\" data-comments-opened=\"0\" data-image-meta=\"{&quot;aperture&quot;:&quot;0&quot;,&quot;credit&quot;:&quot;&quot;,&quot;camera&quot;:&quot;&quot;,&quot;caption&quot;:&quot;&quot;,&quot;created_timestamp&quot;:&quot;0&quot;,&quot;copyright&quot;:&quot;&quot;,&quot;focal_length&quot;:&quot;0&quot;,&quot;iso&quot;:&quot;0&quot;,&quot;shutter_speed&quot;:&quot;0&quot;,&quot;title&quot;:&quot;&quot;}\" data-image-title=\"fig4\" data-image-description=\"\" data-image-caption=\"&lt;p&gt;Figure 5 Reconstruction of LAOS data&lt;\/p&gt;\n\" data-large-file=\"https:\/\/www.andrewsun.net\/panta_rhei\/wp-content\/uploads\/2013\/05\/fig41.png\" src=\"http:\/\/www.andrewsun.net\/panta_rhei\/wp-content\/uploads\/2013\/05\/fig41.png\" alt=\"Figure 5 Reconstruction of LAOS data\" width=\"465\" height=\"363\" class=\"size-full wp-image-5411\"\/><\/a><p id=\"caption-attachment-5411\" class=\"wp-caption-text\">Figure 5 Reconstruction of LAOS data<\/p><\/div>\n<p><i>\u03b3<\/i><sub>0<\/sub> = 250%\u65f6\u5df2\u6709\u660e\u663e\u7684\u975e\u7ebf\u6027\u7c98\u5f39\u6027\u3002<\/p>\n<h3>\u8ba1\u7b97\u975e\u7ebf\u6027\u7c98\u5f39\u6027\u53c2\u6570<\/h3>\n<p>\u6211\u4eec\u5e73\u65f6\u6240\u8bf4\u7684<i>G&#8217;<\/i>\u548c<i>G&#8221;<\/i>\uff0c\u662fFFT\u4e4b\u540e\u7684\u57fa\u9891\u5e45\u503c\u8ba1\u7b97\u7684\u3002\u5728\u7ebf\u6027\u7c98\u5f39\u6027\u6761\u4ef6\u4e0b\uff0cFFT\u4e4b\u540e\u53ea\u6709\u4e00\u4e2a\u57fa\u9891\u5e10\uff0c<i>G&#8217;<\/i>\u548c<i>G&#8221;<\/i>\u662f\u201c\u50a8\u80fd\u6a21\u91cf\u201d\u548c\u201c\u635f\u8017\u6a21\u91cf\u201d\u3002\u4f46\u662f\u5728\u975e\u7ebf\u6027\u7c98\u5f39\u6027\u6761\u4ef6\u4e0b\uff0c<i>G&#8217;<\/i>\u548c<i>G&#8221;<\/i>\u53ea\u662f\u8bb8\u591a<i>n<\/i>\u500d\u9891\u8c10\u6ce2\u4e2d\u7684\u57fa\u9891\u5206\u91cf\uff08<i>n<\/i> = 1\uff09\uff0c\u5b83\u4eec\u4e5f\u6ca1\u6709\u201c\u50a8\u80fd\u201d\u6216\u201c\u635f\u8017\u201d\u7684\u6982\u5ff5\u4e86\u3002\u8fd9\u4e00\u70b9\u8981\u5148\u641e\u6e05\u695a\u3002<\/p>\n<p>\u8ba1\u7b97<i>G&#8217;<\/i>\u548c<i>G&#8221;<\/i>\uff1a<\/p>\n<p><code lang=\"matlab\"><br \/>\ndelta=wrapTo2Pi(delta_n(1)-delta0);<br \/>\nG_p=cos(delta)<em>I_n(1)\/A;<br \/>\nG_pp=sin(delta)<\/em>I_n(1)\/A;<br \/>\n<\/code><\/p>\n<p><i>I<\/i><sub><i>n<\/i>\/1<\/sub>\u4e5f\u53ef\u4ee5\u76f4\u63a5\u8ba1\u7b97\uff1a<\/p>\n<p><code lang=\"matlab\"><br \/>\nIn1=I_n(2:5)\/I_n(1);<br \/>\n<\/code><\/p>\n<h3>\u5982\u4f55\u6c42\u5207\u7ebf<\/h3>\n<p>\u73b0\u5728\u6211\u4eec\u6765\u8ba1\u7b97<i>G<\/i><sub>M<\/sub>\u3001<i>G<\/i><sub>M<\/sub>\u548c<i>G<\/i><sub>k<\/sub>\u53c2\u6570\u3002\u5b83\u4eec\u7684\u5b9a\u4e49\u5df2\u5728\u4e0a\u4e00\u7bc7\u6587\u7ae0\u4e2d\u7ed9\u51fa\u3002\u6839\u636e\u5b9a\u4e49\uff0c\u9700\u8981\u5bf9\u66f2\u7ebf\u8fdb\u884c\u6c42\u5bfc\u3002\u5728MATLAB\u5982\u4f55\u505a\u5462\uff1f\u6309\u5b9a\u4e49\u4e00\u6b65\u6b65\u6765\u3002<\/p>\n<p>\u4e00\u4e2a\u5df2\u7ecf\u79bb\u6563\u5316\u4e86\u7684\u66f2\u7ebf\uff0c\u8981\u5728\u66f2\u7ebf\u4e0a\u67d0\u51e0\u4f55\u4f4d\u7f6e\u6c42\u5207\u7ebf\uff0c\u5f88\u53ef\u80fd\u5e76\u6ca1\u6709\u6570\u636e\u6070\u597d\u843d\u5728\u8fd9\u4e2a\u70b9\u4e0a\uff0c\u53ea\u80fd\u4f7f\u7528\u8fd9\u4e2a\u51e0\u4f55\u4f4d\u7f6e\u90bb\u8fd1\u7684\u4e24\u4e2a\u6570\u636e\u70b9\uff0c\u4ee5\u8fd9\u4e24\u4e2a\u70b9\u6240\u786e\u5b9a\u7684\u76f4\u7ebf\u4f5c\u4e3a\u5207\u7ebf\u3002\u6240\u4ee5\uff0c\u5982\u679c\u4e00\u6761\u66f2\u7387\u8f83\u5927\u7684\u66f2\u7ebf\uff0c\u79bb\u6563\u5316\u7684\u53d6\u6837\u9891\u7387\u53c8\u5f88\u4f4e\uff0c\u90a3\u4e48\u5f88\u53ef\u80fd\u4e24\u4e2a\u6570\u636e\u4e4b\u95f4\u76f8\u9694\u5f88\u8fdc\uff0c\u6309\u4ee5\u4e0a\u529e\u6cd5\u6c42\u51fa\u6765\u7684\u5207\u7ebf\u4e0e\u7406\u60f3\u60c5\u51b5\u5c31\u4f1a\u76f8\u5dee\u5f88\u8fdc\u3002\u4e5f\u5c31\u662f\u8bf4\uff0c\u5bf9\u79bb\u6563\u6570\u636e\u6c42\u5bfc\u7684\u6548\u679c\u975e\u5e38\u4f9d\u8d56\u4e8e\u4fe1\u53f7\u7684\u53d6\u6837\u8d28\u91cf\uff08\u5c31\u662f\u53d6\u6837\u9891\u7387\u591f\u4e0d\u591f\u9ad8\uff09\u3002<\/p>\n<p>\u5176\u6b21\uff0c\u5982\u679c\u4fe1\u53f7\u6709\u566a\u97f3\uff0c\u90a3\u4e48\u4f5c\u51fa\u7684\u5207\u7ebf\u659c\u7387\u5c06\u975e\u5e38\u5bb9\u6613\u53d7\u566a\u97f3\u5f71\u54cd\u3002\u5728\u6570\u503c\u65b9\u6cd5\u4e2d\uff0c\u6c42\u5bfc\u662f\u4e00\u4e2a\u653e\u5927\u566a\u97f3\u7684\u64cd\u4f5c\u3002\u4e00\u4e2a\u4fe1\u53f7\uff0c\u5f88\u53ef\u80fd\u4e0d\u6c42\u5bfc\u7684\u8bdd\uff0c\u566a\u97f3\u8fd8\u5728\u53ef\u4ee5\u63a5\u53d7\u7684\u8303\u56f4\uff1b\u4e00\u65e6\u6c42\u5bfc\u4e4b\u540e\u566a\u97f3\u5c31\u4f7f\u4fe1\u53f7\u65e0\u6cd5\u5206\u8fa8\u3002\u56e0\u6b64\uff0c\u5bf9\u79bb\u6563\u6570\u636e\u6c42\u5bfc\u7684\u6548\u679c\u53c8\u975e\u5e38\u4f9d\u8d56\u4e8e\u4fe1\u53f7\u7684\u4fe1\u566a\u6bd4\u3002<\/p>\n<p>\u56e0\u6b64\u4e3a\u4e86\u6c42\u5f97\u51c6\u786e\u3001\u7a33\u5b9a\u7684\u5bfc\u6570\uff0c\u6211\u4eec\u8981\u91c7\u53d6\u4e00\u7cfb\u5217\u7684\u529e\u6cd5\u3002\u7b2c\u4e00\u5f53\u7136\u5c31\u662f\u6d4b\u8bd5\u7684\u65f6\u5019\u8ba9ADC\u4ee5\u6700\u9ad8\u7684\u91c7\u6837\u9891\u7387\u8fdb\u884c\u91c7\u6837\uff08100 kHz\uff09\u3002<\/p>\n<p>\u7b2c\u4e8c\uff0c\u8fd9\u6837\u9ad8\u7684\u91c7\u6837\u9891\u7387\uff0c\u5b8c\u5168\u53ef\u4ee5\u8fdb\u884c\u964d\u91c7\u6837\uff08down sampling\uff09\u3002\u4f46\u6211\u4eec\u7684\u964d\u91c7\u6837\u65b9\u6cd5\u4e0d\u662f\u50cf\u524d\u6587\u7528\u8fc7\u7684\u90a3\u6837\u7b80\u5355\u5730\u6254\u6389\u90e8\u5206\u6570\u636e\u70b9\u2014\u2014\u8fd9\u6837\u5bf9\u4e8e\u53bb\u566a\u6ca1\u6709\u4efb\u4f55\u6548\u679c\u2014\u2014\u800c\u662f\u6bcf\u51e0\u4e2a\u6570\u636e\u70b9\u505a\u4e00\u6b21\u5e73\u5747\u503c\uff0c\u8fd9\u6837\u7684\u505a\u6cd5\u53eb<a href=\"http:\/\/en.wikipedia.org\/wiki\/Decimation_(signal_processing)\">decimation<\/a>\uff0c\u5b83\u7684\u6548\u679c\u76f8\u5f53\u4e8e\u4f7f\u6837\u54c1\u7ecf\u8fc7\u4e00\u4e2a\u4f4e\u901a\u6ee4\u6ce2\u54c1\uff0c\u628a\u9ad8\u4e8e\u4e00\u5b9a\u9891\u7387\u7684\u4fe1\u53f7\u6d88\u9664\u6389\u3002\u5982\u679c\u6211\u4eec\u6bcf<i>N<\/i>\u4e2a\u6570\u636e\u53d6\u4e00\u4e2a\u5e73\u5747\u503c\uff0c\u90a3\u4e48decimation\u4e4b\u540e\u7684\u53d6\u6837\u9891\u7387\u5c31\u662f100000\/<i>N<\/i> Hz\u3002\u4e00\u5f00\u59cb\uff0c\u7528\u8fdc\u9ad8\u4e8e\u9700\u8981\u7684\u53d6\u6837\u9891\u7387\u53d6\uff0c\u79f0\u4f5c\u8fc7\u53d6\u6837\uff08<a href=\"http:\/\/en.wikipedia.org\/wiki\/Oversampling\">oversampling<\/a>\uff09\u3002Oversampling\u548cdecimation\u662f\u4fe1\u53f7\u91c7\u96c6\u4e2d\u7684\u4e00\u4e2a\u57fa\u672c\u64cd\u4f5c\uff0c\u4f5c\u4e3a\u4e00\u79cd\u63d0\u4f9b\u4fe1\u566a\u6bd4\u7684\u6807\u51c6\u6b65\u9aa4\u3002\u4f7f\u7528FT Measurement\u91c7\u96c6\u7684\u6d41\u53d8\u6570\u636e\u7684\u65f6\u5019\uff0c\u8be5\u8f6f\u4ef6\u662f\u540c\u65f6\u505a\u4e86oversampling\u548cdecimation\u7684\uff0c\u6700\u7ec8\u5f97\u5230\u7684\u6587\u672c\u6570\u636e\u6587\u4ef6\u7684\u91c7\u6837\u9891\u7387\u662fdecimation\u4e4b\u540e\u7684\u91c7\u6837\u9891\u7387\u3002\u8fd9\u65b9\u9762\u5185\u5bb9\uff0c\u4e5f\u53ef\u4ee5\u53c2\u8003\u6211\u7684\u535a\u58eb\u8bba\u6587\u7684\u7b2c\u4e8c\u7ae0\u3002<\/p>\n<p>\u7b2c\u4e09\uff0c\u6211\u4eec\u6309\u7167LAOS\u7684\u5047\u8bbe\uff08\u5e94\u529b\u6ce2\u578b\u53ea\u6709\u5947\u6b21\u8c10\u6ce2\uff09\u5bf9\u4fe1\u53f7\u8fdb\u884c\u91cd\u6784\uff0c\u7528\u4e00\u4e2a\u5149\u6ed1\u7684\u3001\u516c\u5f0f\u8ba1\u7b97\u7684\u66f2\u7ebf\u6765\u4ee3\u66ff\u5b9e\u9a8c\u6d4b\u5f97\u7684\u3001\u5e26\u6709\u566a\u97f3\u7684\u66f2\u7ebf\u3002\u91cd\u6784\u66f2\u7ebf\u662f\u5b8c\u5168\u6ca1\u6709\u566a\u97f3\u7684\u3002\u8fd9\u8fd8\u4e0d\u591f\u2014\u2014<\/p>\n<p>\u7b2c\u56db\uff0c\u7531\u4e8e\u4fe1\u53f7\u6709\u5f88\u591a\u4e2a\u5468\u671f\uff0c\u90a3\u4e9b\u8fc7\u96f6\u70b9\u3001\u6700\u503c\u70b9\u4e4b\u7c7b\u7684\u51e0\u4f55\u4f4d\u7f6e\uff0c\u4fe1\u53f7\u4e0d\u6b62\u7ecf\u8fc7\u4e00\u6b21\u3002\u90a3\u4e48\uff0c\u6211\u4eec\u5c31\u628a\u6bcf\u6b21\u7ecf\u8fc7\u7684\u8fd9\u4e9b\u4f4d\u7f6e\u6240\u80fd\u4f5c\u51fa\u7684\u5207\u7ebf\u659c\u7387\u90fd\u7b97\u51fa\u6765\uff0c\u7136\u540e\u5bf9\u8fd9\u4e48\u591a\u4e2a\u5468\u671f\u5f97\u5230\u7684\u659c\u7387\u66f2\u4e00\u4e2a\u5e73\u5747\u503c\uff0c\u8fdb\u4e00\u6b65\u6d88\u9664\u4e0d\u540c\u5468\u671f\u5904\u7684\u7ec6\u5fae\u5dee\u522b\u3002<\/p>\n<p>\u53ea\u6709\u505a\u8db3\u4ee5\u4e0a\u56db\u4e2a\u65b9\u9762\uff0c\u624d\u80fd\u6bd4\u8f83\u4fdd\u8bc1\u5730\u5bf9\u7edd\u5927\u591a\u6570\u5b9e\u6d4b\u7684LAOS\u6570\u636e\u8fdb\u884c\u51c6\u786e\u53ef\u9760\u7684\u6c42\u5bfc\u64cd\u4f5c\u3002<\/p>\n<p>\u5728MATLAB\u4e2d\u5982\u4f55\u5728\u91cd\u6784\u7684Lissajous\u66f2\u7ebf\u4e0a\u627e\u5230\u8981\u4f5c\u5207\u7ebf\u7684\u51e0\u4f55\u4f4d\u70b9\uff1f\u6839\u636e\u5b9a\u4e49\uff0c<i>G<\/i><sub>M<\/sub>\u8981\u627e<i>\u03b3<\/i> = 0\uff0c<i>G<\/i><sub>L<\/sub>\u8981\u627e<i>\u03b3<\/i> = <i>\u03b3<\/i><sub>0<\/sub>\uff0c<i>G<\/i><sub>k<\/sub>\u8981\u627e<i>\u03c3<\/i> = 0\u3002\u6211\u4eec\u9700\u8981\u786e\u5b9a\u8fd9\u4e9b\u51e0\u4f55\u4f4d\u7f6e\u90bb\u8fd1\u7684\u4e24\u4e2a\u6570\u636e\u70b9\u5904\u5728\u6570\u636e\u5217\u4e2d\u7684\u7b2c\u51e0\u884c\u3002\u4ee5<i>G<\/i><sub>M<\/sub>\u7684\u8ba1\u7b97\u4e3a\u4f8b\uff08\u627e<i>\u03b3<\/i> = 0\uff09\u3002\u8fd9\u76f8\u5f53\u4e8e\u8981\u627e\u6570\u636ex_rec\u4e2d\u53d6\u503c\u7ecf\u8fc7\u96f6\u4f4d\u7684\u884c\u3002\u800c\u4e14\uff0c\u6211\u4eec\u53ea\u5173\u5fc3\u4ece\u5c0f\u4e8e\u96f6\u53d8\u6210\u5927\u4e8e\u96f6\u7684\u5730\u65b9\uff08\u8fd9\u91cc\u9ed8\u9ed8\u5047\u8bbe\u4e86x_rec\u662f\u6ca1\u6709\u76f4\u6d41\u5206\u91cf\u7684\uff0c\u5982\u679c\u6709\u76f4\u6d41\u5206\u91cf\uff0cx_rec\u6ce2\u5f62\u7684\u96f6\u4f4d\u5c31\u4e0d\u843d\u5728\u53d6\u503c\u4e3a\u96f6\u5904\uff0c\u9664\u975e\u53e6\u628aDC\u5206\u91cf\u51cf\u53bb\uff09\u3002\u9996\u5148\uff0c\u6211\u4eec\u628ax_rec\u6570\u636e\u6240\u6709\u5927\u4e8e\u96f6\u7684\u503c\u6807\u4e3a1\uff0c\u5c0f\u4e8e\u96f6\u7684\u503c\u6807\u4e3a0\u3002<\/p>\n<p><code lang=\"matlab\"><br \/>\nA=x_rec;<br \/>\nA(A&gt;0)=1;<br \/>\nA(A&lt;0)=0;<br \/>\n<\/code><\/p>\n<p>\u5728A\u8fd9\u4e2a\u4e34\u65f6\u53d8\u91cf\uff0c\u51e1\u662f\u5bfc\u6570\u4e0d\u4e3a\u96f6\u7684\u5730\u65b9\u5c31\u662f\u8f6c\u6298\u70b9\uff08\u4e0d\u662f\u4ece1\u53d8\u52300\u5c31\u662f\u4ece0\u53d8\u52301\uff09\uff0c\u8fd9\u4e9b\u4e0d\u4e3a\u96f6\u7684\u5bfc\u6570\uff0c\u4e0d\u662f\u7b49\u4e8e1\u5c31\u662f\u7b49\u4e8e-1\u3002\u7531\u4e8e\u6211\u4eec\u53ea\u5173\u5fc3x_rec\u4e2d\u4ece\u5c0f\u4e8e0\u53d8\u6210\u5927\u4e8e\u96f6\u7684\u5730\u65b9\uff0c\u6240\u4ee5\u6211\u4eec\u76f8\u5f53\u4e8e\u53ea\u5173\u5fc3A\u7684\u5bfc\u6570\u7b49\u4e8e1\u7684\u5730\u65b9\u3002<\/p>\n<p><code lang=\"matlab\"><br \/>\nzero_ind=find(diff(A)&gt;0);<br \/>\n<\/code><\/p>\n<p>\u4ee5\u4e0a\u7528\u5230\u7684\u4e00\u4e9b\u7528\u903b\u8f91\u5f0f\u8c03\u7528\u77e9\u9635\u5355\u5143\u7684\u65b9\u6cd5\uff0c\u548cfind\u547d\u4ee4\u7b49\uff0c\u53ef\u4ee5\u81ea\u5df1\u590d\u4e60MATLAB\u7684help\u3002zero_ind\u5c31\u662fx_rec\u4e2d\u53d6\u503c\u4ece\u8d1f\u5230\u6b63\u7684\u7b2c\u4e00\u4e2a\u6570\u636e\uff0c\u5373\u5b83\u662f\u8d1f\u7684\uff0c\u7136\u540e\u7b2czero_ind+1\u662f\u6b63\u7684\u3002\u6211\u4eec\u53ef\u4ee5\u4e34\u65f6\u4f5c\u4e2a\u56fe\u770b\u770b\uff0c\u6211\u4eec\u627e\u5230\u7684zero_ind\u4f4d\u7f6e\u90fd\u5bf9\u4e0d\u5bf9\uff1a<\/p>\n<p><code lang=\"matlab\"><br \/>\nplot(1:length(x_rec),x_rec,'-',zero_ind,zeros(length(zero_ind),1),'o') % Figure 6<br \/>\n<\/code><\/p>\n<div id=\"attachment_5418\" style=\"width: 484px\" class=\"wp-caption alignnone\"><a href=\"http:\/\/www.andrewsun.net\/panta_rhei\/wp-content\/uploads\/2013\/05\/fig6.png\"><img loading=\"lazy\" decoding=\"async\" aria-describedby=\"caption-attachment-5418\" data-attachment-id=\"5418\" data-permalink=\"https:\/\/www.andrewsun.net\/panta_rhei\/archives\/5377\/fig6\" data-orig-file=\"https:\/\/www.andrewsun.net\/panta_rhei\/wp-content\/uploads\/2013\/05\/fig6.png\" data-orig-size=\"474,363\" data-comments-opened=\"0\" data-image-meta=\"{&quot;aperture&quot;:&quot;0&quot;,&quot;credit&quot;:&quot;&quot;,&quot;camera&quot;:&quot;&quot;,&quot;caption&quot;:&quot;&quot;,&quot;created_timestamp&quot;:&quot;0&quot;,&quot;copyright&quot;:&quot;&quot;,&quot;focal_length&quot;:&quot;0&quot;,&quot;iso&quot;:&quot;0&quot;,&quot;shutter_speed&quot;:&quot;0&quot;,&quot;title&quot;:&quot;&quot;}\" data-image-title=\"fig6\" data-image-description=\"\" data-image-caption=\"&lt;p&gt;Figure 6 Effect of zero finding&lt;\/p&gt;\n\" data-large-file=\"https:\/\/www.andrewsun.net\/panta_rhei\/wp-content\/uploads\/2013\/05\/fig6.png\" src=\"http:\/\/www.andrewsun.net\/panta_rhei\/wp-content\/uploads\/2013\/05\/fig6.png\" alt=\"Figure 6 Effect of zero finding\" width=\"474\" height=\"363\" class=\"size-full wp-image-5418\"\/><\/a><p id=\"caption-attachment-5418\" class=\"wp-caption-text\">Figure 6 Effect of zero finding<\/p><\/div>\n<p>\u6c42\u5bfc\u3001\u53d6\u5e73\u5747\uff0c\u5f97\u5230<i>G<\/i><sub>M<\/sub>\uff1a<\/p>\n<p><code lang=\"matlab\"><br \/>\nG_M_raw=(y_rec(zero_ind+1)-y_rec(zero_ind)).\/(A(zero_ind+1)-A(zero_ind));<br \/>\nG_M=mean(G_M_raw);<br \/>\n<\/code><\/p>\n<p>\u6211\u4eec\u53ef\u4ee5\u518d\u4e34\u65f6\u4f5c\u4e2a\u56fe\u770b\u770b\u8fd9\u4e2a\u5207\u7ebf\u53d6\u51c6\u4e86\u6ca1\u6709\u3002\u4f46\u4e3a\u4f5c\u8fd9\u4e2a\u56fe\uff0c\u8981\u5148\u786e\u5b9a\u771f\u5b9e\u7684\u4f4d\u70b9\u5728\u54ea\u513f\uff08\u4e0d\u80fd\u8fd8\u7528\u90a3\u4e24\u4e2a\u90bb\u8fd1\u6570\u636e\u70b9\uff09\u3002\u8fd9\u4e2a\u70b9\uff0c\u5e94\u8be5\u662f\u4e24\u4e2a\u76f8\u90bb\u70b9\u6240\u786e\u5b9a\u7684\u76f4\u7ebf\u4e0ex = 0\u76f4\u7ebf\u7684\u4ea4\u70b9\u3002\u540c\u6837\uff0c\u8fd9\u4e2a\u4ea4\u70b9\u4e5f\u53ef\u4ee5\u901a\u8fc7\u591a\u4e2a\u5468\u671f\u6c42\u5e73\u5747\u800c\u66f4\u4e3a\u51c6\u786e\u5730\u786e\u5b9a\u3002\u6700\u7ec8\u8981\u4f5c\u7684\u5207\u7ebf\uff0c\u5c31\u662f\u4e00\u6761\u8fc7\u8fd9\u4e00\u4ea4\u70b9\uff0c\u659c\u7387\u4e3a<i>G<\/i><sub>M<\/sub>\u7684\u76f4\u7ebf\uff0c\u5229\u7528\u7b80\u5355\u89e3\u6790\u51e0\u4f55\u77e5\u8bc6\u5373\u53ef\u4f5c\u51fa\uff1a<\/p>\n<p><code lang=\"matlab\"><br \/>\ny_m_raw=-G_M_raw.<em>x_rec(zero_ind+1)+y_rec(zero_ind+1);<br \/>\ny_m=mean(y_m_raw);<br \/>\nlx=min(x_rec):0.01:max(x_rec);<br \/>\nly=G_M.<\/em>lx+y_m;<br \/>\nplot(x_rec,y_rec,'-b',lx,ly,'-r') % Figure 7<br \/>\n<\/code><\/p>\n<div id=\"attachment_5422\" style=\"width: 475px\" class=\"wp-caption alignnone\"><a href=\"http:\/\/www.andrewsun.net\/panta_rhei\/wp-content\/uploads\/2013\/05\/fig7.png\"><img loading=\"lazy\" decoding=\"async\" aria-describedby=\"caption-attachment-5422\" data-attachment-id=\"5422\" data-permalink=\"https:\/\/www.andrewsun.net\/panta_rhei\/archives\/5377\/fig7\" data-orig-file=\"https:\/\/www.andrewsun.net\/panta_rhei\/wp-content\/uploads\/2013\/05\/fig7.png\" data-orig-size=\"465,363\" data-comments-opened=\"0\" data-image-meta=\"{&quot;aperture&quot;:&quot;0&quot;,&quot;credit&quot;:&quot;&quot;,&quot;camera&quot;:&quot;&quot;,&quot;caption&quot;:&quot;&quot;,&quot;created_timestamp&quot;:&quot;0&quot;,&quot;copyright&quot;:&quot;&quot;,&quot;focal_length&quot;:&quot;0&quot;,&quot;iso&quot;:&quot;0&quot;,&quot;shutter_speed&quot;:&quot;0&quot;,&quot;title&quot;:&quot;&quot;}\" data-image-title=\"fig7\" data-image-description=\"\" data-image-caption=\"&lt;p&gt;Figure 7 Effect of G_M calculation&lt;\/p&gt;\n\" data-large-file=\"https:\/\/www.andrewsun.net\/panta_rhei\/wp-content\/uploads\/2013\/05\/fig7.png\" src=\"http:\/\/www.andrewsun.net\/panta_rhei\/wp-content\/uploads\/2013\/05\/fig7.png\" alt=\"Figure 7 Effect of G_M calculation\" width=\"465\" height=\"363\" class=\"size-full wp-image-5422\"\/><\/a><p id=\"caption-attachment-5422\" class=\"wp-caption-text\">Figure 7 Effect of G_M calculation<\/p><\/div>\n<p><i>G<\/i><sub>L<\/sub>\u8981\u627e<i>\u03b3<\/i> = <i>\u03b3<\/i><sub>0<\/sub>\uff0c\u5373\u627ex_rec\u4e2d\u7684\u6700\u503c\u3002\u5148\u5bf9x_rec\u8fdb\u884c\u6c42\u5bfc\uff0c\u95ee\u9898\u5c31\u8fd8\u539f\u6210\u627ex_rec\u6c42\u5bfc\u540e\u7684\u8fc7\u96f6\u4f4d\uff0c\u9664\u4e86\u591a\u4e00\u6b65\u6c42\u5bfc\u4e4b\u5916\uff0c\u5176\u4f59\u8ddf\u521a\u624d\u7684\u4ee3\u7801\u5b8c\u5168\u76f8\u540c\u3002\u6ce8\u610f\u7684\u65f6\uff0cy_rec\u6709\u660e\u663e\u7684\u76f4\u6d41\u5206\u91cf\uff0c\u8ba1\u7b97\u65f6\u8981\u51cf\u53bb\u3002<\/p>\n<p><code lang=\"matlab\"><br \/>\nA=diff(x_rec);<br \/>\nA(A&gt;0)=1;<br \/>\nA(A&lt;0)=0;<\/code><\/p>\n<p><code lang=\"matlab\">zero_ind=find(diff(A)&lt;0);<\/p>\n<p><\/code><code lang=\"matlab\">G_L_raw=(y_rec(zero_ind)-DC).\/x_rec(zero_ind);<br \/>\nG_L=mean(G_L_raw);<br \/>\n<\/code><\/p>\n<p><i>G<\/i><sub>k<\/sub>\u662f\u627e<i>\u03c3<\/i> = 0\uff1a<\/p>\n<p><code lang=\"matlab\"><br \/>\nA=y_rec-DC;<br \/>\nA(A&gt;0)=1;<br \/>\nA(A&lt;0)=0;<br \/>\nzero_ind=find(diff(A)&gt;0);<\/code><\/p>\n<p><code lang=\"matlab\">A=y_rec-DC;<br \/>\nG_k_raw=(A(zero_ind+1)-A(zero_ind)).\/(x_rec(zero_ind+1)-x_rec(zero_ind));<\/p>\n<p><\/code><code lang=\"matlab\">G_k=mean(G_k_raw);<br \/>\n<\/code><\/p>\n<p>\u81f3\u6b64\uff0c\u6211\u5df2\u7ecf\u5b8c\u6574\u5730\u4ecb\u7ecd\u4e86\u5982\u4f55\u4ece\u5b9e\u9a8c\u83b7\u5f97\u7684LAOS\u6570\u636e\u6c42\u51fa\u76f8\u5e94\u7684\u975e\u7ebf\u6027\u7c98\u5f39\u6027\u53c2\u6570\u3002\u6211\u518d\u603b\u7ed3\u4e00\u4e0b\u6d41\u7a0b\uff1a<\/p>\n<ol>\n<li>\u505a\u5b9e\u9a8c\uff0c\u8bbe\u5b9aADC\u91c7\u96c6\u53c2\u6570\u8fdb\u884c\u6570\u636e\u91c7\u96c6\uff08\u540c\u65f6\u5df2\u8fdb\u884coversampling\u548cdecimation\uff0c\u89c4\u5b9a\u4e86\u4fe1\u53f7\u7684<i>f<\/i><sub>s<\/sub>\uff09<\/li>\n<li>\u901a\u8fc7\u5bf9\u5e94\u53d8\u4fe1\u53f7\u8fdb\u884c\u7c97\u4f30\u548c\u6b63\u5f26\u62df\u5408\uff0c\u83b7\u5f97\u5b9e\u9a8c\u7684\u51c6\u786e\u6d4b\u8bd5\u9891\u7387<\/li>\n<li>\u5bf9\u5e94\u53d8\u548c\u5e94\u529b\u4fe1\u53f7\u8fdb\u884c\u91cd\u6784<\/li>\n<li>\u6309\u7167\u5b9a\u4e49\u6c42\u5f97\u5404\u975e\u7ebf\u6027\u7c98\u5f39\u6027\u53c2\u6570<\/li>\n<\/ol>\n<p>\u5982\u679c\u5bf9\u5b9e\u9a8c\u4f53\u7cfb\u4ee5\u4e00\u7cfb\u5217\u7684\u5e94\u53d8\u5e45\u5ea6\u8fdb\u884c\u4e86LAOS\u5b9e\u9a8c\uff0c\u7136\u540e\u60f3\u8003\u5bdf\u975e\u7ebf\u6027\u53c2\u6570\u968f\u5e94\u53d8\u5e45\u5ea6\u7684\u53d8\u5316\uff1b\u90a3\u4e48\uff0c\u53ef\u4ee5\u5bf9\u6bcf\u4e2a\u5e94\u53d8\u5e45\u5ea6\u5f97\u5230\u7684LAOS\u6570\u636e\u505a\u4ee5\u4e0a\u540c\u6837\u7684\u64cd\u4f5c\uff0c\u65e2\u7f16\u5199\u4e00\u4e2a\u5faa\u73af\u7ed3\u6784\u6765\u5b8c\u6210\u3002\u8fd9\u6837\u7684\u529e\u6cd5\u5c06\u5728\u540e\u9762\u7684\u6587\u7ae0\u4e2d\u770b\u5230\u4f8b\u5b50\uff0c\u6b64\u5904\u4e0d\u5355\u72ec\u4e3e\u4f8b\u4e86\u3002\u540e\u9762\u7684\u6587\u7ae0\u4e3b\u8981\u4ecb\u7ecd\u5982\u4f55\u7528\u6d41\u53d8\u5b66\u6a21\u578b\u7684\u7ed3\u679c\uff08\u4f8b\u5982Giesekus\u6a21\u578b)\u6765\u62df\u5408\u5b9e\u9a8c\u6570\u636e\u3002<\/p>\n<h2>References<\/h2>\n    <ol>\n    <li><a name='ITEM-5377-1'><\/a>\nK. Hyun, M. Wilhelm, C.O. Klein, K.S. Cho, J.G. Nam, K.H. Ahn, S.J. Lee, R.H. Ewoldt, and G.H. McKinley, \"A review of nonlinear oscillatory shear tests: Analysis and application of large amplitude oscillatory shear (LAOS)\", <i>Progress in Polymer Science<\/i>, vol. 36, pp. 1697-1753, 2011. <a href=\"http:\/\/dx.doi.org\/10.1016\/j.progpolymsci.2011.02.002\">http:\/\/dx.doi.org\/10.1016\/j.progpolymsci.2011.02.002<\/a>\n\n\n<\/li>\n<\/ol>\n\n<\/div> <!-- kcite-section 5377 -->","protected":false},"excerpt":{"rendered":"<p>[mathjax] \u901a\u8fc7\u4e0a\u4e00\u7bc7\u6211\u4eec\u5df2\u7ecf\u5b66\u4f1a\u600e\u6837\u901a\u8fc7Fourier\u53d8\u6362\u91cd\u6784\u5e94\u53d8\u548c\u5e94\u529b\u7684\u6ce2\u5f62\u3002\u81f3\u5c11In\/1\u662f\u5df2\u7ecf\u53ef\u4ee5\u76f4\u63a5\u7528Fourier\u53d8\u6362\u7684\u7ed3\u679c\u8ba1\u7b97\u4e86\u3002\u672c\u6587\u5148\u4ecb\u7ed3\u5b9e\u9645\u5b9e\u9a8c\u6570\u636e\u7684\u5bfc\u5165\uff0c\u518d\u7ee7\u7eed\u4e0a\u4e00\u7bc7\u7684\u8bdd\u9898\u4ecb\u7ecd\u5982\u4f55\u8ba1\u7b97In\/1\u548c\u5176\u4f59\u7684LAOS\u53c2\u6570\u3002 LAOS\u5b9e\u9a8c\u662f\u600e\u4e48\u5b9e\u65bd\u7684 \u6211\u4eec\u662f\u5728TA ARES-RFS\u6d41\u53d8\u4eea\u4e0a\u505aLAOS\u5b9e\u9a8c\u3002\u516c\u53f8\u7684\u540d\u5b57\uff1aTA Instruments\u3002\u8fd9\u662f\u4e00\u53f0\u5e94\u53d8\u63a7\u5236\u578b\u6d41\u53d8\u4eea\uff08strain-controlled rheometer\uff09\uff0c\u76f8\u6bd4\u4e4b\u4e0b\u540c\u516c\u53f8\u7684AR-G2\u5219\u662f\u5e94\u529b\u63a7\u5236\u578b\uff08stress-controlled\uff09\u3002\u8fd9\u4e2a\u5c0f\u518c\u5b50\u4e0a\u4ecb\u7ecd\u4e86ARES\u548cAR-G2\u4e24\u53f0\u6d41\u53d8\u4eea\u7684\u7279\u70b9\uff0c\u5176\u4e2d\u7684\u539f\u7406\u56fe\u548c\u5177\u4f53\u53c2\u6570\u53ef\u4ee5\u7528\u5728\u6bd5\u4e1a\u8bba\u6587\u4e2d\u3002\u8fdb\u884cLAOS\u5b9e\u9a8c\u9700\u8981\u6d41\u53d8\u4eea\u6301\u7eed\u5bf9\u6837\u54c1\u65bd\u52a0\u6b63\u5f26\u5e94\u53d8\uff0c\u6211\u4eec\u662f\u5229\u7528\u6d41\u53d8\u4eea\u63a7\u5236\u8f6f\u4ef6TA Orchestrator 7.2.1\u81ea\u5e26\u7684\u6d4b\u8bd5\u6a21\u5f0fdynamic time sweep\u6765\u63a7\u5236\u6d41\u53d8\u4eea\u8fdb\u884c\u8fd9\u4e00\u64cd\u4f5c\u3002Dynamic time sweep\u662f\u56fa\u5b9a\u632f\u8361\u7684\u5e94\u53d8\u5e45\u5ea6\u03b30\u548c\u9891\u7387\u03c9\uff0c\u6d4b\u91cfG&#8217;\u548cG&#8221;\u968f\u65f6\u95f4\u53d8\u5316\u7684\u6d4b\u8bd5\uff0c\u6240\u4ee5\u6b63\u9002\u5408\u6211\u4eec\u3002\u5728Orchestrator\u8f6f\u4ef6\u4e2d\u8bbe\u5b9a\u597ddynamic time sweep\u7684\u5e94\u53d8\u548c\u9891\u7387\uff0c\u4eea\u5668\u5c31\u4f1a\u4ee5\u76f8\u5e94\u7684\u6b63\u5f26\u51fd\u6570\u53bb\u63a7\u5236\u9a6c\u8fbe\u4e86\u3002\u6b64\u65f6\uff0c\u6211\u4eec\u9700\u8981\u9a6c\u4e0a\u4ece\u4eea\u5668\u80cc\u540e\u7684\u6a21\u62df\u8f93\u51fa\u7aef\u53e3\u540c\u65f6\u8bfb\u51fa\u4eea\u5668\u7684\u6d4b\u91cf\u4fe1\u53f7\uff0c\u5e76\u7528\u4e00\u4e2a\u6570\u6a21\u8f6c\u6362\u5668\uff08analog-to-digital converter, ADC\uff09\u8f6c\u6362\u6210\u6570\u5b57\u4fe1\u53f7\uff0c\u8f93\u5165\u5230\u8ba1\u7b97\u673a\u3002\u6211\u4eec\u7528\u7684ADC\u662fNI USB-9215A\uff0c\u8981\u901a\u8fc7\u7535\u8111\u6765\u63a7\u5236\u5b83\u4f55\u65f6\u5f00\u59cb\u548c\u505c\u6b62\u91c7\u6837\uff0c\u4ee5\u53ca\u4ee5\u591a\u5927\u7684\u91c7\u6837\u9891\u7387\u8fdb\u884c\u91c7\u6837\u3002\u8bb8\u591a\u8f6f\u4ef6\u90fd\u53ef\u4ee5\u901a\u8fc7\u5b83\u7684\u9a71\u52a8\u7a0b\u5e8f\u63a5\u53e3\u6765\u5b9e\u65bd\u63a7\u5236\uff08MATLAB\u672c\u8eab\u5c31\u53ef\u4ee5\uff09\uff0c\u5728LAOS\u5b9e\u9a8c\u4e2d\u6211\u4eec\u7528\u4e00\u4e2aLabView\u5f00\u53d1\u7684\u5de5\u5177FT Meassurement\u6765\u91c7\u96c6\u6570\u636e\u3002\u56e0\u6b64\uff0c\u6211\u4eec\u7528\u4e00\u53f0\u7535\u8111\uff0c\u7528\u4e24\u4e2a\u8f6f\u4ef6\u5206\u800c\u63a7\u5236\u4e0d\u540c\u7684\u8fc7\u7a0b\u3002Orchestrator\u63a7\u5236\u6d41\u53d8\u4eea\u7684\u8fd0\u4f5c\uff0c\u800cFT Meassurement\u63a7\u5236ADC\u3002\u8fd9\u4e00\u6d41\u7a0b\u56fe\u53ef\u53c2\u8003\u548c\u4e2d\u7684\u7528\u56fe\u3002\u5177\u4f53\u4fe1\u53f7\u7ebf\u63a5\u6cd5\u548c\u5904\u7406\u65b9\u5f0f\u89c1\u4e0b\u9762\u7684PPT\uff08\u53ef\u4e0b\u8f7d\uff09\u3002 ARES\u6a21\u62df\u8f93\u51fa View more presentations or Upload your own. \u4e0a\u7bc7\u6587\u7ae0\u4e5f\u8bf4\u8fc7\uff0c\u4ece\u6d41\u53d8\u4eea\u91c7\u96c6\u5230\u7684\u4e00\u4e2a\u662f\u9a6c\u8fbe\u4f4d\u79fb\u7684\u7535\u538b\u4fe1\u53f7\uff0c\u53e6\u4e00\u4e2a\u662f\u529b\u77e9\u7684\u7535\u538b\u4fe1\u53f7\uff0c\u5b83\u4eec\u90fd\u8981\u4e58\u4ee5\u4e00\u4e2a\u7cfb\u6570\uff0c\u624d\u662f\u5e94\u53d8\u548c\u5e94\u529b\u3002\u4eceARES\u6d41\u53d8\u4eea\u7684\u8bf4\u4e66\u4e2d\u53ef\u4ee5\u67e5\u5230\u80cc\u677f\u8f93\u51fa\u4fe1\u53f7\u7684\u5177\u4f53\u60c5\u51b5\uff1a TORQUE OUT\uff1a\u4ece0\u5230\u6ee1\u91cf\u7a0b\uff0c\u5bf9\u5e94\u7535\u538b\u662f0 ~ 5 V\u3002\u7531\u4e8e\u8f6c\u77e9\u53ef\u4ee5\u6709\u4e24\u4e2a\u65b9\u5411\uff0c\u6240\u4ee5\u603b\u7684\u7535\u538b\u8303\u56f4\u5c31\u662f-5 ~ +5 V STRAIN OUT\uff1a\u867d\u7136\u6807\u8bb0\u662fSTRAIN\uff0c\u4f46\u5176\u5b9e\u53ea\u662f\u9a6c\u8fbe\u8f6c\u52a8\u7684\u89d2\u4f4d\u79fb\u3002\u4ece0 ~ 0.5 rad\u5bf9\u5e94\u7535\u538b\u662f0~5V\uff0c\u8003\u8651\u4e24\u4e2a\u8f6c\u52a8\u65b9\u5411\uff0c\u603b\u7535\u538b\u8303\u56f4\u662f-5~+5 V TORQUE OUT\u7684\u201c\u6ee1\u91cf\u7a0b\u201d\u5230\u5e95\u662f\u591a\u5c11\u5462\uff1f\u7531\u4e8e\u6211\u4eec\u7684ARES\u6709\u4e24\u4e2a\u6863\u4f4d\u7684\u529b\u77e9\u4f20\u611f\u5668\u3002Xducer 1\u7684\u4f20\u611f\u5668\u53eb\u505a\u201c20g FRT\u201d\u300220g\u662f\u6307\u8be5\u6863\u4f4d\u7684\u6700\u5927\u91cf\u7a0b\u662f20 g\u00b7cm\uff0c\u529b\u77e9\u7684\u4e00\u4e2a\u975eSI\u5355\u4f4d\uff0cSI\u5355\u4f4d\u662fN\u00b7m\u30021 g\u00b7cm = 98.066E-6 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\u6309\u7167\u6ce2\u5f62\u4fe1\u53f7\u5206\u6790\u7684\u6807\u51c6\u6765\u8bbe\u8ba1LAOS\u8f6f\u4ef6 \u76ee\u524d\u6211\u7684\u60f3\u6cd5\u662f\uff0c\u4ee5IEEE Standard for Terminology and Analog-Digital Converters\uff08IEEE Std 1241-2000\uff09\u548cIEEE Standard for Digitizing Waveform Recorders\uff08IEEE Std\u2026","rel":"","context":"In &quot;\u5de5\u4f5c\u7b14\u8bb0&quot;","block_context":{"text":"\u5de5\u4f5c\u7b14\u8bb0","link":"https:\/\/www.andrewsun.net\/panta_rhei\/archives\/category\/personal\/%e5%b7%a5%e4%bd%9c%e7%ac%94%e8%ae%b0"},"img":{"alt_text":"","src":"","width":0,"height":0},"classes":[]},{"id":5297,"url":"https:\/\/www.andrewsun.net\/panta_rhei\/archives\/5297","url_meta":{"origin":5377,"position":1},"title":"Fourier\u53d8\u6362\uff08\u4e8c\uff09","author":"Andrew","date":"2013\u5e744\u670823\u65e5","format":false,"excerpt":"[mathjax] \u4e0a\u4e00\u7bc7\u4ecb\u7ecd\u4e86\u7528Fourier\u53d8\u6362\u6765\u91cd\u6784\u4e00\u4e2a\u672a\u77e5\u6b63\u5f26\u4fe1\u53f7\u7684\u65b9\u6cd5\u3002\u672c\u7bc7\u4ecb\u7ecd\u5bf9\u4e8e\u672a\u77e5\u975e\u6b63\u5f26\u4fe1\u53f7\u7684\u60c5\u51b5\u3002 \u5927\u5e45\u632f\u8361\u526a\u5207\u7684\u53c2\u6570 \u5927\u5e45\u632f\u8361\u526a\u5207\u5b9e\u9a8c\u4ea7\u751f\u7684\u6ce2\u5f62\u662f\u975e\u6b63\u5f26\u4fe1\u53f7\uff0c\u975e\u6b63\u5f26\u662f\u975e\u7ebf\u6027\u7c98\u5f39\u6027\u7684\u7279\u70b9\u3002\u6240\u4ee5\u5bf9\u975e\u7ebf\u6027\u7c98\u5f39\u6027\u7a0b\u5ea6\u7684\u8868\u5f81\uff0c\u5c31\u662f\u5bf9\u6ce2\u5f62\u6b63\u5f26\u5f62\u72b6\u504f\u79bb\u7a0b\u5ea6\u7684\u8868\u5f81\u3002\u5173\u4e8e\u5927\u5e45\u632f\u8361\u526a\u5207\u548c\u975e\u7ebf\u6027\u7c98\u5f39\u6027\u7684\u539f\u7406\u4e0e\u5b9e\u8df5\uff0c\u53ef\u89c1Hyhn\u7b49\u7684\u7efc\u8ff0\uff0c\u6216\u8005\u53c2\u9605\u6211\u7684\u535a\u58eb\u5b66\u4f4d\u8bba\u6587\u7b2c1.2.1\u8282\u3001\u7b2c1.3\u8282\u548c\u7b2c2\u7ae0\u3002\u672c\u6587\u53ea\u89e3\u51b3MATLAB\u7f16\u7a0b\u5b9e\u73b0\u95ee\u9898\u3002 \u5927\u5e45\u632f\u8361\u526a\u5207\uff08LAOS\uff09\u5b9e\u9a8c\u4e2d\uff0c\u6211\u4eec\u4ece\u6d41\u53d8\u4eea\u540c\u65f6\u83b7\u53d6\u4e24\u4e2a\u4fe1\u53f7\u3002\u4e00\u4e2a\u662f\u5e94\u53d8\u7684\u4fe1\u53f7\uff0c\u4e00\u4e2a\u662f\u5e94\u529b\u7684\u4fe1\u53f7\uff08\u4e8b\u5b9e\u4e0a\uff0c\u4e00\u4e2a\u662f\u9a6c\u8fbe\u4f4d\u79fb\u4fe1\u53f7\uff0c\u53e6\u4e00\u4e2a\u662f\u529b\u77e9\u4fe1\u53f7\uff0c\u5b83\u4eec\u90fd\u8981\u4e58\u4ee5\u4e00\u4e2a\u7cfb\u6570\uff0c\u624d\u662f\u5e94\u53d8\u548c\u5e94\u529b\u3002\u6b64\u6587\u5148\u7565\u53bb\u8fd9\u4e00\u4e8b\u5b9e\u4e86\uff09\u3002\u5728\u5e94\u53d8\u63a7\u5236\u7684\u5b9e\u9a8c\u4e2d\uff0c\u6211\u4eec\u65bd\u52a0\u4e00\u4e2a\u6b63\u5f26\u7684\u5e94\u53d8\uff0c\u6d4b\u91cf\u5e94\u529b\u7684\u54cd\u5e94\uff0c\u5373 $$\\begin{cases}\\gamma\\left(t\\right)=\\sin\\omega t\\\\ \\sigma\\left(t\\right)=\\sum_{n=0:\\text{odd}}^\\infty\\sigma_n\\sin\\left(\\omega t+\\delta_n\\right)\\end{cases}$$\u7531\u6b64\u5f0f\u53ef\u5b9a\u4e49LAOS\u5b9e\u9a8c\u7ed3\u679c\u7684\u8868\u5f81\u53c2\u6570\uff0c\u4ee5\u53ca\uff0c\u6765\u8868\u5f81\u975e\u7ebf\u6027\u7c98\u5f39\u6027\u7684\u7a0b\u5ea6\uff08\u5373\u504f\u79bb\u6b63\u5f26\u51fd\u6570\u7684\u7a0b\u5ea6\u3002\u6b64\u5916\uff0c\u6211\u4eec\u8fd8\u4f1a\u4ee5\u5bf9\u4f5c\u56fe\uff08\u53c2\u6570\u65b9\u7a0b\u4f5c\u56fe\uff09\uff0c\u5f97\u5230Lissajous\u66f2\u7ebf\u3002\u7136\u540e\u7528\u66f2\u7ebf\u7684\u5f62\u72b6\u7279\u5f81\u6765\u8868\u5f81\u975e\u7ebf\u6027\u7c98\u5f39\u6027\u7684\u7a0b\u5ea6\uff08\u5373\u66f2\u7ebf\u504f\u79bb\u692d\u5706\u7684\u7a0b\u5ea6\uff09\u3002\u63cf\u8ff0\u66f2\u7ebf\u5f62\u72b6\u7279\u5f81\uff0c\u5f80\u5f80\u5c31\u662f\u5404\u79cd\u5404\u6837\u7684\u5207\u7ebf\u659c\u7387\uff08\u53ef\u81ea\u884c\u4e0a\u7f51\u641c\u7d22\u590d\u4e60\u53c2\u6570\u65b9\u7a0b\u6c42\u5bfc\uff09\u3002\u5728LAOS\u4e2d\u5e38\u7528\uff1a$$G_\\text{M}=\\left.\\frac{d\\sigma}{d\\gamma}\\right|_{\\gamma=0}$$$$G_\\text{L}=\\frac{\\sigma{\\gamma_0}}{\\gamma_0}$$$$G_\\text{k}=\\left.\\frac{d\\sigma}{d\\gamma}\\right|_{\\sigma=0}$$ MATLAB\u7f16\u7a0b\u6b65\u9aa4 \u5728\u8be6\u7ec6\u4ecb\u7ecdMATLAB\u4ee3\u7801\u4e4b\u524d\uff0c\u5148\u603b\u7ed3\u4e00\u4e0b\u6211\u4eec\u8981\u5b8c\u6210\u4ec0\u4e48\u4efb\u52a1\uff0c\u8ddf\u4ece\u54ea\u4e9b\u6b65\u9aa4\u3002\u6211\u4eec\u7684\u4efb\u52a1\u5c31\u662f\u8981\u4ece\u5e94\u529b\u548c\u5e94\u53d8\u7684\u4fe1\u53f7\u8ba1\u7b97\u51fa\u4e0a\u8ff0\u7684\u8fd9\u4e48\u591a\u53c2\u6570\u3002\u5b9e\u9a8c\u65f6\uff0c\u6211\u4eec\u4f1a\u89c4\u5b9a\u5e94\u53d8\u7684\u5e45\u5ea6\u548c\u9891\u7387\uff0c\u4f46\u662f\uff0c\u7531\u4e8e\u4eea\u5668\u8bef\u5dee\uff0c\u5b9e\u9645\u65bd\u52a0\u5728\u6837\u54c1\u4e0a\u7684\u5e94\u53d8\u5e45\u5ea6\u548c\u9891\u7387\uff0c\u672a\u5fc5\u5b8c\u5168\u7b49\u4e8e\u7684\u547d\u4ee4\u503c\u3002\u5c3d\u7ba1\u8fd9\u4e00\u8bef\u5dee\u975e\u5e38\u5c0f\uff0c\u4f46\u4ece\u505a\u6cd5\u4e0a\u6211\u4eec\u8fd8\u662f\u8981\u4ee5\u5b9e\u9645\u5e94\u53d8\u4fe1\u53f7\u4e3a\u51c6\u3002\u6240\u4ee5\uff0c\u6211\u4eec\u9996\u5148\u8981\u5bf9\u5b9e\u9645\u5e94\u53d8\u4fe1\u53f7\u8fdb\u884c\u5224\u65ad\uff0c\u83b7\u5f97\u5b9e\u9645\u7684\u5e94\u53d8\u5e45\u5ea6\u548c\u9891\u7387\u3002\u5982\u4f55\u5224\u65ad\u4e00\u4e2a\u672a\u77e5\u6b63\u5f26\u4fe1\u53f7\u7684\u632f\u5e45\u3001\u9891\u7387\u548c\u76f8\u4f4d\u7684\u65b9\u6cd5\u5df2\u7ecf\u5728\u4e0a\u4e00\u7bc7\u6587\u7ae0\u4e2d\u4ecb\u7ecd\u4e86\u3002 \u7136\u540e\uff0c\u5c31\u8981\u5904\u7406\u5e94\u529b\u7684\u4fe1\u53f7\u3002\u4e3a\u4e86\u83b7\u5f97\u548c\u540c\u6837\u9700\u8981\u5bf9\u8fdb\u884cfft\u5904\u7406\uff0c\u65b9\u6cd5\u8ddf\u4e0a\u4e00\u7bc7\u6587\u7ae0\u4ecb\u7ecd\u7684\u7c7b\u4f3c\uff0c\u533a\u522b\u53ea\u5728\u4e8e\u6211\u4eec\u9664\u4e86\u8981\u83b7\u5f97\u57fa\u9891\u7684\u5e45\u503c\u548c\u76f8\u4f4d\u4e4b\u5916\uff0c\u8fd8\u8981\u83b7\u5f97\u9ad8\u6b21\u8c10\u6ce2\u7684\u5e45\u503c\u548c\u76f8\u4f4d\u3002\u7406\u8bba\u4e0a\u6765\u8bf4\uff0c\u4f46\u662f\u5b9e\u9645\u4e0a\u6211\u4eec\u6839\u636e\u9700\u8981\u53d6\u6709\u9650\u7684n\u4e2a\u9ad8\u6b21\u8c10\u6ce2\uff0c\u5c31\u53ef\u4ee5\u6bd4\u8f83\u51c6\u786e\u5730\u91cd\u6784\u51fa\u7684\u6ce2\u5f62\u4e86\u3002\u63d0\u9192\u4e00\u4e0b\uff0c\u5b9a\u4e49\u5f0f\u91cc\u5e94\u53d8\u662f\u4e00\u4e2a\u96f6\u76f8\u4f4d\u7684\u6807\u51c6\u6b63\u5f26\u51fd\u6570\uff0c\u4f46\u5b9e\u9645\u91cd\u6784\u7684\u5e94\u53d8\u6ce2\u5f62\u53ef\u80fd\u4f1a\u6709\u975e\u96f6\u7684\u76f8\u4f4d\uff0c\u8fd9\u65f6\uff0c\u5e94\u529b\u7684\u5404\u4e2a\u8c10\u6ce2\u7684\u76f8\u4f4d\u8981\u90fd\u51cf\u53bb\u5e94\u53d8\u7684\u76f8\u4f4d\uff0c\u624d\u662f\u6211\u4eec\u8981\u6c42\u7684\u3002 Lissajous\u66f2\u7ebf\u7684\u5404\u79cd\u5bfc\u6570\uff0c\u8981\u540c\u65f6\u5728\u548c\u90fd\u91cd\u6784\u4e86\u4e4b\u540e\uff0c\u518d\u8fdb\u884c\u6c42\u5bfc\u8ba1\u7b97\u5f97\u5230\u3002\u603b\u800c\u8a00\u4e4b\uff0c\u8981\u5b8c\u6210\u4ee5\u4e0b\u4e09\u4e2a\u6b65\u9aa4\uff1a \u91cd\u6784\u5e94\u53d8\uff0c\u83b7\u5f97\u3001\u548c\u76f8\u4f4d \u91cd\u6784\uff0c\u83b7\u5f97\u548c\uff0c\u8ba1\u7b97 \u7528\u91cd\u6784\u7684\u548c\u4f5cLissajous\u66f2\u7ebf\uff0c\u4ee5\u53ca\u8ba1\u7b97\u3001\u548c \u91cd\u6784\u548c MATLAB\u5e2e\u52a9\u6587\u4ef6\u91ccfft\u547d\u4ee4\u7684\u6761\u76ee\u6709\u4e00\u4e2a\u8303\u4f8b\uff0c\u5e94\u8be5\u80fd\u89e3\u51b3\u5927\u90e8\u5206\u95ee\u9898\u4e86\u3002\u5176\u4e2d\u5728coherent sampling\uff08\u89c1\u4e0a\u7bc7\u6587\u7ae0\uff09\u5904\uff0c\u8303\u4f8b\u7528next power of 2\uff0c\u5176\u5b9e\u6ca1\u6709\u5fc5\u8981\u3002\u4e0b\u9762\u7684\u4ee3\u7801\uff0c\u6211\u5c31\u4e0d\u591a\u4f5c\u89e3\u91ca\u4e86\u3002 clear all clc % the strain signal fs=1000; % sampling frequency t=0:1\/fs:30.2; % the time series of the strain signal t=t(:); % convert to colume vector w=5; %\u2026","rel":"","context":"In &quot;\u5de5\u4f5c\u7b14\u8bb0&quot;","block_context":{"text":"\u5de5\u4f5c\u7b14\u8bb0","link":"https:\/\/www.andrewsun.net\/panta_rhei\/archives\/category\/personal\/%e5%b7%a5%e4%bd%9c%e7%ac%94%e8%ae%b0"},"img":{"alt_text":"Figure 1 Parts of the strain and the stress signals","src":"https:\/\/i0.wp.com\/www.andrewsun.net\/panta_rhei\/wp-content\/uploads\/2013\/04\/fig1.png?resize=350%2C200","width":350,"height":200,"srcset":"https:\/\/i0.wp.com\/www.andrewsun.net\/panta_rhei\/wp-content\/uploads\/2013\/04\/fig1.png?resize=350%2C200 1x, https:\/\/i0.wp.com\/www.andrewsun.net\/panta_rhei\/wp-content\/uploads\/2013\/04\/fig1.png?resize=525%2C300 1.5x"},"classes":[]},{"id":9177,"url":"https:\/\/www.andrewsun.net\/panta_rhei\/archives\/9177","url_meta":{"origin":5377,"position":2},"title":"\u5728\u7535\u5b50\u8ba1\u7b97\u673a\u4e4b\u524d\u7684Fourier\u5206\u6790","author":"Andrew","date":"2025\u5e743\u670830\u65e5","format":"aside","excerpt":"[latexpage] \u5982\u679c\u6211\u4eec\u8981\u5bf9\u4e00\u4e2a\u5468\u671f\u4fe1\u53f7\u8fdb\u884cFourier\u7ea7\u6570\u5206\u6790\uff0c\u90a3\u4e48\u6211\u4eec\u662f\u5047\u5b9a\u8be5\u4fe1\u53f7\u53ef\u4ee5\u8868\u793a\u6210\\[f\\left(x\\right)=\\sum_{n=-\\infty}^\\infty c_n e^{\\mathrm{i}2\\pi n x\/P}\\]\u5176\u4e2d\\[c_n=\\frac{1}{P}\\int_0^P f\\left(x\\right)e^{-\\mathrm{i} 2\\pi n x\/P}\\mathrm{d}x\\] \u5728\u4eca\u5929\uff0c\u6211\u4eec\u7684\u5b9e\u9a8c\u4fe1\u53f7\u57fa\u672c\u90fd\u5df2\u7ecf\u6570\u5b57\u5316\uff0c\u5728\u7535\u5b50\u8ba1\u7b97\u673a\u4e2d\u4e00\u79d2\u949f\u4e0d\u5230\u5c31\u505a\u5b8c\u4e86\u4e00\u4e2a\u5feb\u901fFourier\u53d8\u6362\u8ba1\u7b97\u3002\u4f46\u662f\u5728\u4e0a\u4e16\u7eaa50~60\u5e74\u4ee3\uff0c\u7535\u5b50\u8ba1\u7b97\u673a\u8fd8\u6ca1\u53d1\u660e\u4e4b\u524d\uff0c\u5b9e\u9a8c\u7ed3\u679c\u672c\u8eab\u5c31\u53ef\u80fd\u662f\u901a\u8fc7X-Y\u8bb0\u5f55\u4eea\u6216\u53cc\u7b14\u8bb0\u5f55\u4eea\u753b\u5728\u5750\u6807\u7eb8\u4e0a\u7684\u3002\u5f53\u65f6\u7684\u4eba\u662f\u600e\u6837\u5bf9\u8fd9\u4e48\u4e00\u6bb5\u58a8\u8ff9\u8fdb\u884cFourier\u7ea7\u6570\u5206\u6790\u7684\u5462\uff1f\u6211\u4eec\u53ef\u4ee5\u770b\u5230\uff0cFourier\u7ea7\u6570\u7684\u5404\u4e2a\u7cfb\u6570$c_n$\u662f\u4e00\u4e2a\u79ef\u5206\u3002\u5728\u90a3\u4e2a\u5e74\u4ee3\uff0c\u79ef\u5206\u53ef\u4ee5\u4f7f\u7528\u6b27\u62c9\u6cd5\u6570\u503c\u6c42\u89e3\u3002\u5728\u6b64\u4e4b\u524d\uff0c\u9700\u8981\u5c06\u88ab\u79ef\u51fd\u6570\u8fdb\u884c\u4eba\u5de5\u91c7\u6837\uff08sampling\uff09\u79bb\u6563\u5316\u3002\u56e0\u6b64\u8fd9\u662f\u4e00\u4e2a\u5f88\u7e41\u7410\u7684\u4efb\u52a1\u3002 \u5c0f\u91ce\u6728\u91cd\u6cbb\uff08Shigeharu Onogi\uff09\u53ef\u80fd\u662f\u65e5\u672c\u6700\u65e9\u5bf9\u975e\u7ebf\u6027\u7c98\u5f39\u6027\u6d41\u4f53\u7684\u6b63\u5f26\u632f\u8361\u6d4b\u8bd5\u7ed3\u679c\u4f5c\u8c10\u6ce2\u5206\u6790\u7684\u7814\u7a76\u8005\u3002\u4ed6\u5f53\u65f6\u4f30\u8ba1\u5c31\u662f\u8fd9\u4e48\u505a\u7684\u3002 \u5728\u7f8e\u56fd\uff0cW. 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1960\u5e74\u4ee3\uff0c\u6070\u597d\u662f\u6a21\u62df\u6280\u672f\u7684\u98a0\u5cf0\u65f6\u671f\u3002\u6a21\u62df\u8ba1\u7b97\u7535\u8def\u80fd\u80fd\u505a\u5f88\u591a\u4e8b\u60c5\u3002\u7531\u6d41\u53d8\u4eea\u5f97\u51fa\u7684\u6ce2\u5f62\u4fe1\u53f7\uff0c\u53ef\u901a\u8fc7\u76f8\u5173\u5668\u4e0e\u7ed9\u5b9a\u7684\u6ce2\u5f62\u6bd4\u8f83\uff0c\u8f93\u51fa\u7684\u7ed3\u679c\u662f\u4e0e\u7ed9\u5b9a\u6ce2\u5f62\u7684\u5185\u79ef\u3002\u8fd9\u6837\u5c31\u53ef\u4ee5\u901a\u8fc7\u8bbe\u5b9a\u53c2\u8003\u6ce2\u5f62\u4fe1\u53f7\uff0c\u4ece\u539f\u59cb\u4fe1\u53f7\u4e2d\u63d0\u53d6\u76f8\u5e94\u7684\u5206\u91cf\uff0c\u4ece\u800c\u5b9e\u73b0\u8c10\u6ce2\u5206\u6790\u3002\u4f8b\u5982\uff0cQueen's Collage\u673a\u68b0\u5de5\u7a0b\u7cfb\u7684Harris\u548cBogie\u3002 1967\u5e74\uff0cBrenner\u7684\u6797\u80af\u5b9e\u9a8c\u5ba4\u62a5\u544a\u7ed9\u51fa\u4e86Cooley\u548cTukey\u7684\u5feb\u901fFourier\u53d8\u6362\u7684Fortran\u7a0b\u5e8f\u3002\u51ef\u65af\u897f\u50a8\u5927\u5b66\u5316\u5b66\u7cfb\u7684Dodge\u548cKrieger\u57281971\u5e74\u5c31\u7528\u4e0a\u8fd9\u4e2a\u65b9\u6cd5\u6765\u8fdb\u884c\u8c10\u6ce2\u5206\u6790\u4e86\uff0c\u6b63\u5f0f\u8fdb\u5165\u4e86\u6570\u5b57\u65f6\u4ee3\u3002","rel":"","context":"In &quot;\u4ee5tag\u5206\u7c7b\u7684\u6587\u7ae0&quot;","block_context":{"text":"\u4ee5tag\u5206\u7c7b\u7684\u6587\u7ae0","link":"https:\/\/www.andrewsun.net\/panta_rhei\/archives\/category\/tagged"},"img":{"alt_text":"","src":"","width":0,"height":0},"classes":[]},{"id":3868,"url":"https:\/\/www.andrewsun.net\/panta_rhei\/archives\/3868","url_meta":{"origin":5377,"position":3},"title":"TA\u65b0\u6d41\u53d8\u4eea\u4ea7\u54c1\u7cfb\u5217Discovery Hybrid Rheometers","author":"Andrew","date":"2011\u5e749\u67082\u65e5","format":false,"excerpt":"\u540e\u77e5\u540e\u89c9\u7684\u6211\u5230\u4eca\u5929\u624d\u77e5\u9053TA\u51fa\u4e86\u65b0\u7684\u6d41\u53d8\u4eea\uff0c\u7f29\u5199\u53ebDHR\u3002\u4ece\u67b6\u6784\u4e0a\u770b\u5e94\u8be5\u662f\u4e00\u53f0\u5e94\u529b\u63a7\u5236\u578b\u6d41\u53d8\u4eea\u3002\u4e8e\u662fAR\u7cfb\u5217\u8981\u62dc\u62dc\u4e86\uff1f\u4f7f\u7528AR-G2\u8ba9\u6211\u6709\u4e09\u70b9\u4e0d\u723d\uff1a\u57fa\u672c\u65e0\u6548\u7684\u60ef\u91cf\u8f83\u6b63\u3002\u6211\u6ca1\u6709\u9047\u5230\u4efb\u4f55\u4e00\u79cd\u60c5\u51b5\u4e0b\u52a8\u6001\u626b\u9891\u80fd\u505a\u5230\u03c9 > 70 rad\/s\u5404\u79cd\u9636\u8dc3\u6d4b\u8bd5\u63a7\u5236\u91cf\u8fbe\u5230\u7a33\u6001\u7684\u65f6\u95f4\u592a\u957f\uff0c\u800c\u4e14\u6709\u602a\u73b0\u8c61\u3002\u5c24\u5176\u662f\u5e94\u53d8\u63a7\u5236\u3002\u4f8b\u5982\u505a\u9636\u8dc3\u5e94\u53d8\u901f\u7387\u7684\u65f6\u5019\uff0c\u5e94\u53d8\u901f\u7387\u503c\u7a33\u5b9a\u4e00\u4f1a\u513f\u4e4b\u540e\u603b\u662f\u8981\u51fa\u4e00\u4e2a\u5c0f\u5cf0\u518d\u7ee7\u7eed\u771f\u6b63\u5730\u7ef4\u6301\u7a33\u5b9a\u3002\u8fd9\u4e2a\u5c0f\u5cf0\u4e0d\u662f\u4fe1\u53f7\uff0c\u662f\u771f\u7684\u5e94\u53d8\u901f\u7387\uff0c\u56e0\u4e3a\u5bfc\u81f4\u6d4b\u5f97\u7684\u5e94\u529b\u4e5f\u51fa\u4e2a\u5c0f\u5cf0\u4e86\u3002\u4e0d\u80fd\u83b7\u5f97\u539f\u59cb\u6ce2\u578b\uff0c\u505a\u4e0d\u4e86LAOS\uff08\u54ea\u6015\u662f\u5e94\u529b\u63a7\u5236\u578b\u7684LAOS\uff09\u5176\u5b9e\u7b2c\u4e00\u4e2a\u60c5\u51b5\uff0c\u5bf9\u4e8e\u4f4e\u7c98\u5ea6\u6837\u54c1\u57fa\u81f3\u505a\u4e0d\u5230\u03c9 > 10 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measurements\u201d\uff0c\u4e0d\u77e5\u9053\u5230\u5e95\u662f\u89e3\u51b3\u4e86\u5565\u3002\u4ee5\u524d\u7684LAOS\u600e\u4e48impure\u6cd5\u4e86\u3002\u5176\u5b9e\u7528\u5e94\u529b\u63a7\u5236\u578b\u6d41\u53d8\u4eea\u505a\u5e94\u53d8\u63a7\u5236LAOS\u6709\u4e2a\u95ee\u9898\u5c31\u662f\u53cd\u9988\u56de\u8def\u662f\u5426\u5229\u7528\u4e86\u7ebf\u6027\u7c98\u5f39\u6027\u7684\u524d\u63d0\u3002\u8fd9\u4e2a\u5176\u5b9e\u4e5f\u4e0d\u6210\u95ee\u9898\uff0c\u56e0\u4e3a\u6211\u5b8c\u5168\u53ef\u4ee5\u6539\u505a\u5e94\u529b\u63a7\u5236\u7684LAOS\uff0c\u83b7\u5f97\u9ad8\u6b21\u8c10\u6ce2\u67d4\u91cf\u800c\u4e0d\u662f\u6a21\u91cf\u3002\u771f\u6b63\u7684\u95ee\u9898\u5728\u4e8e\u7528\u6237\u80fd\u5426\u53d6\u6a21\u62df\u4fe1\u53f7\u81ea\u5df1\u5e72\u3002AR\u7cfb\u5217\u662f\u4e0d\u884c\u7684\u3002\u800c\u4e14TA\u5e94\u8be5\u901a\u8fc7ARES\u7cfb\u5217\u5c1d\u5230\u4e86\u4fdd\u7559\u6a21\u62df\u8f93\u51fa\u7684\u751c\u5934\u3002\u7531\u4e8e\u8fd9\u4e1c\u897f\u7684\u5b58\u5728\u591a\u5c11\u7814\u7a76\u5c0f\u7ec4\u5e2eTA\u505a\u4e86\u65b0\u4e1c\u897f\uff08\u4e0d\u4ec5\u4ec5\u662fLAOS\uff09\uff0c\u4fdd\u4f4f\u4e86\u5e94\u53d8\u63a7\u5236\u6d41\u53d8\u4eea\u7684\u65b0\u9c9c\u5ea6\u3002\u76f8\u53cdAR\u7cfb\u5217\u7531\u4e8e\u6ca1\u6709\u5f80\u8fd9\u4e2a\u65b9\u5411\u8d70\u7684\u53ef\u80fd\uff0c\u53cd\u800c\u8ba9\u5b89\u4e1c\u5e15\u7b49\u5728\u6613\u7528\u6027\u4e0a\u505a\u6587\u7ae0\u8d85\u8fc7\u4e86\u3002","rel":"","context":"In &quot;\u4ee5tag\u5206\u7c7b\u7684\u6587\u7ae0&quot;","block_context":{"text":"\u4ee5tag\u5206\u7c7b\u7684\u6587\u7ae0","link":"https:\/\/www.andrewsun.net\/panta_rhei\/archives\/category\/tagged"},"img":{"alt_text":"","src":"","width":0,"height":0},"classes":[]},{"id":1031,"url":"https:\/\/www.andrewsun.net\/panta_rhei\/archives\/1031","url_meta":{"origin":5377,"position":4},"title":"\u4e3a\u4ec0\u4e48G&#039;&#039;\u662f\u8d1f\u503c\uff1f","author":"Andrew","date":"2010\u5e745\u670825\u65e5","format":false,"excerpt":"\u4e3b\u9898\u56de\u5f52\u5230\u6d41\u53d8\u5b66\u4e00\u4e0b\u3002\u4f17\u6240\u5468\u77e5\uff08\u7ebf\u6027\uff09\u7c98\u5f39\u6027\u662f\u5904\u4e8eHookian\u5f39\u6027\u548cNewtonian\u7c98\u6027\u8fd9\u4e24\u4e2a\u6781\u7aef\u4e4b\u95f4\u7684\u6027\u8d28\u3002\u5bf9Hookian\u5f39\u6027\u4f53\uff08Hookian\u5f39\u7c27\u6a21\u578b\uff09\u65bd\u52a0\u6b63\u5f26\u5f62\u53d8\uff0c\u6d4b\u5230\u7684\u662f\u540c\u76f8\u7684\u6b63\u5f26\u5e94\u529b\uff1b\u5411Newtonian\u7c98\u6d41\u4f53\uff08Newtonian\u7c98\u58f6\uff09\u65bd\u52a0\u6b63\u5f26\u5f62\u53d8\u901f\u7387\uff0c\u6d4b\u5230\u7684\u662f\u540c\u76f8\u7684\u6b63\u5f26\u5e94\u529b\u3002\u5411\u4e00\u4e2a\u7ebf\u6027\u7c98\u5f39\u6027\u6837\u54c1\u65bd\u52a0\u6b63\u5f26\u5f62\u53d8\uff0c\u6d4b\u5230\u7684\u662f\u76f8\u4f4d\u89d2\u4e3a[eq]\\delta[\/eq]\u7684\u6b63\u5f26\u5e94\u529b\uff1a[eq]\\gamma_0 \\sin \\left ( \\omega t+\\delta \\right )[\/eq]\u3002 \u6700\u4e3a\u4eba\u719f\u6089\u7684\u6d41\u53d8\u5b66\u6d4b\u8bd5\uff08\u4e5f\u662f\u6700\u591a\u4e0d\u61c2\u6d41\u53d8\u7684\u4eba\u77e5\u9053\u8981\u505a\u7684\u6d4b\u8bd5\uff09\u5c31\u662f[eq]G'[\/eq]\u3001[eq]G''[\/eq]~[eq]\\omega[\/eq]\u66f2\u7ebf\uff0c\u8fd9\u4e2a\u4e5f\u53eb\u505a\u201c\u7c98\u5f39\u8c31\u201d\u3002\u6211\u66fe\u7ecf\u8be6\u7ec6\u89e3\u91ca\u8fc7[eq]G'[\/eq]\u548c[eq]G''[\/eq]\u5230\u5e95\u662f\u600e\u4e48\u6765\u7684\u3002\u5178\u578b\u7ebf\u578b\u805a\u5408\u7269\u7c98\u5f39\u8c31\u5982\u4e0b\u56fe\uff1a \u4e0b\u56fe\u662f\u6211\u914d\u5236\u7684\u5408\u6210\u9502\u85fb\u571fLaponite\u51dd\u80f6\u7684\u7c98\u5f39\u8c31\uff0c\u53d1\u73b0[eq]G''[\/eq]\u5728\u9ad8\u9891\u5904\u51fa\u73b0\u8d1f\u503c\u3002\u4e0b\u9762\u662f\u5bf9\u8fd9\u4e2a\u4e0d\u6b63\u5e38\u73b0\u8c61\u7684\u89e3\u91ca\u3002 \u4e00\u53f0\u5e94\u53d8\u63a7\u5236\u578b\u6d41\u53d8\u4eea\u82e5\u8981\u7ed9\u51fa\u8fd9\u6837\u7684\u56fe\uff0c\u5c31\u8981\u7ed9\u6837\u54c1\u65bd\u52a0\u4e00\u5b9a\u9891\u7387[eq]\\omega[\/eq]\u548c\u5e45\u5ea6[eq]\\gamma[\/eq]\u7684\u6b63\u5f26\u5e94\u53d8[eq]\\gamma \\left ( t \\right ) = \\gamma_0 \\sin \\left ( \\omega t \\right)[\/eq]\uff0c\u7136\u540e\u5939\u5177\u6240\u8fde\u63a5\u7684\u529b\u5b66\u4f20\u611f\u5668\u8bb0\u5f55\u6837\u54c1\u5411\u5939\u5177\u65bd\u52a0\u7684\u8f6c\u77e9\uff0c\u5e76\u6839\u636e\u5939\u5177\u5f62\u72b6\u548cGap\u503c\u6362\u7b97\u6210\u5e94\u53d8[eq]\\sigma \\left ( t \\right )[\/eq]\uff0c\u5728\u7ebf\u6027\u7c98\u5f39\u6027\u6761\u4ef6\u4e0b[eq]\\sigma \\left ( t \\right )=\\sigma_0 \\sin \\left ( \\omega t + \\delta \\right )[\/eq]\u3002\u4eea\u54c1\u4ec5\u9700\u4e14\u5fc5\u987b\u51c6\u786e\u6d4b\u91cf\u51fa\u4e24\u4e2a\u503c\uff1a[eq]\\sigma_0[\/eq]\uff08\u4ece\u5728\u8f6c\u77e9\u6570\u636e\u4e2d\u627e\u5230\u7684\u6700\u503c\u6362\u7b97\uff09\u548c[eq]\\delta[\/eq]\uff08\u901a\u8fc7\u6bd4\u8f83\u8f6c\u77e9\u6570\u636e\u548c\u5e94\u53d8\u6570\u636e\u7684\u76f8\u4f4d\u5dee[eq]\\Delta t[\/eq]\u6362\u7b97\uff0c\u89c1\u7b2c1\u5e45\u56fe\uff09\u3002\u5176\u4e2d\uff0c[eq]\\Delta t=\\frac{\\delta}{\\omega}[\/eq]\u3002\u5176\u4ed6\u8bf8\u5982[eq]G'[\/eq]\u3001[eq]\\eta'[\/eq]\u4e4b\u7c7b\u7684\uff0c\u90fd\u662f\u4ece\u8fd9\u4e24\u4e2a\u6570\u636e\u7b97\u51fa\u6765\u7684\u3002\u4f8b\u5982[eq]G''=\\frac {\\sigma_0}{\\gamma_0} \\sin \\left( \\omega \\right\u2026","rel":"","context":"In &quot;\u4ee5tag\u5206\u7c7b\u7684\u6587\u7ae0&quot;","block_context":{"text":"\u4ee5tag\u5206\u7c7b\u7684\u6587\u7ae0","link":"https:\/\/www.andrewsun.net\/panta_rhei\/archives\/category\/tagged"},"img":{"alt_text":"\u5c0f\u5e45\u632f\u8361\u529b\u5b66\u54cd\u5e94","src":"https:\/\/i0.wp.com\/www.andrewsun.net\/xiangge\/wp-content\/uploads\/2010\/05\/11-300x188.png?resize=350%2C200","width":350,"height":200},"classes":[]},{"id":9185,"url":"https:\/\/www.andrewsun.net\/panta_rhei\/archives\/9185","url_meta":{"origin":5377,"position":5},"title":"\u201c\u6d41\u53d8\u6d4b\u89d2\u4eea\u201d","author":"Andrew","date":"2025\u5e743\u670831\u65e5","format":false,"excerpt":"\u5361\u5c14\u00b7\u9b4f\u68ee\u4f2f\u683c\uff08Karl Weissenberg\uff09\u7814\u5236\u7684\u6d41\u53d8\u4eea\uff0c\u5f53\u65f6\u79f0\u4e3a\u6d41\u53d8\u6d4b\u89d2\u4eea\uff08rheogoniometer\uff09\u3002\u9b4f\u68ee\u4f2f\u683c\u7684\u6d41\u53d8\u4eea\u5e38\u5e26\u7740\u4ed6\u7684\u59d3\u4e00\u9f50\u8868\u8ff0\u4e3aWeissenberg 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