{"id":2903,"date":"2011-04-29T01:10:08","date_gmt":"2011-04-28T17:10:08","guid":{"rendered":"http:\/\/www.andrewsun.net\/panta_rhei\/?p=2903"},"modified":"2011-04-29T01:11:52","modified_gmt":"2011-04-28T17:11:52","slug":"ares%e7%9b%b8%e4%bd%8d%e8%a7%92%e6%b5%8b%e9%87%8f%e5%92%8c%e5%ba%94%e5%8f%98%e6%8e%a7%e5%88%b6%e9%97%ae%e9%a2%98","status":"publish","type":"post","link":"https:\/\/www.andrewsun.net\/panta_rhei\/archives\/2903","title":{"rendered":"ARES\u76f8\u4f4d\u89d2\u6d4b\u91cf\u548c\u5e94\u53d8\u63a7\u5236\u95ee\u9898"},"content":{"rendered":"
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\"\u76f8\u4f4d\u89d2\u68c0\u67e5\"<\/a>

\u76f8\u4f4d\u89d2\u68c0\u67e5<\/p><\/div>\n

\u4ece\u53a6\u5927\u501f\u4e86\u4e00\u5957torsion rectangular\u5939\u5177\u4ee5\u4fbf\u68c0\u67e5ARES\u7684\u76f8\u4f4d\u89d2\u6d4b\u8bd5\u95ee\u9898\uff0c\u505a\u4e86\u4e24\u5929\u5b9e\u9a8c\uff0c\u7ed3\u679c\u5df2\u603b\u7ed3\u53d1\u7ed9TA\u516c\u53f8\u7684\u5ba2\u670d\u90ae\u7bb1\u4e86\u3002\u4ee5\u4e0b\u662f\u603b\u7ed3\u5185\u5bb9\uff1a<\/p>\n\n<\/div> ","protected":false},"excerpt":{"rendered":"

\u4ece\u53a6\u5927\u501f\u4e86\u4e00\u5957torsion rectangular\u5939\u5177\u4ee5\u4fbf\u68c0\u67e5ARES\u7684\u76f8\u4f4d\u89d2\u6d4b\u8bd5\u95ee\u9898\uff0c\u505a\u4e86\u4e24\u5929\u5b9e\u9a8c\uff0c\u7ed3\u679c\u5df2\u603b\u7ed3\u53d1\u7ed9TA\u516c\u53f8\u7684\u5ba2\u670d\u90ae\u7bb1\u4e86\u3002\u4ee5\u4e0b\u662f\u603b\u7ed3\u5185\u5bb9\uff1a<\/p>\n","protected":false},"author":1,"featured_media":0,"comment_status":"open","ping_status":"open","sticky":false,"template":"","format":"standard","meta":{"inline_featured_image":false,"_jetpack_newsletter_access":"","_jetpack_dont_email_post_to_subs":false,"_jetpack_newsletter_tier_id":0,"_jetpack_memberships_contains_paywalled_content":false,"_jetpack_memberships_contains_paid_content":false,"footnotes":"","jetpack_publicize_message":"","jetpack_publicize_feature_enabled":true,"jetpack_social_post_already_shared":false,"jetpack_social_options":{"image_generator_settings":{"template":"highway","default_image_id":0,"font":"","enabled":false},"version":2},"jetpack_post_was_ever_published":false},"categories":[212],"tags":[240],"class_list":["post-2903","post","type-post","status-publish","format-standard","hentry","category-tagged","tag-rheometer"],"jetpack_publicize_connections":[],"jetpack_featured_media_url":"","jetpack_sharing_enabled":true,"jetpack_shortlink":"https:\/\/wp.me\/p1aPvF-KP","jetpack-related-posts":[{"id":5297,"url":"https:\/\/www.andrewsun.net\/panta_rhei\/archives\/5297","url_meta":{"origin":2903,"position":0},"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 "\u5de5\u4f5c\u7b14\u8bb0"","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":4706,"url":"https:\/\/www.andrewsun.net\/panta_rhei\/archives\/4706","url_meta":{"origin":2903,"position":1},"title":"\u6ce2\u5f62\u91cd\u6784\u4ee3\u7801","author":"Andrew","date":"2012\u5e745\u670828\u65e5","format":false,"excerpt":"\u5bf9\u771f\u5b9e\u4e16\u754c\u7684\u4fe1\u53f7\u8fdb\u884c\u6c42\u5bfc\uff0c\u9700\u8981\u5148\u5927\u5e45\u63d0\u9ad8\u4fe1\u53f7\u7684\u4fe1\u566a\u6bd4\uff0c\u5426\u5219\u6c42\u5bfc\u8fd0\u7b97\u5c31\u662f\u4e00\u4e2a\u566a\u97f3\u653e\u5927\u5668\u3002\u5bf9\u4e8eLAOS\u5b9e\u9a8c\u7684\u4fe1\u53f7\uff0c\u7531\u4e8e\u5047\u8bbe\u5176\u4e3a\u4e00\u7cfb\u5217\u5947\u6b21\u8c10\u6ce2\u7684\u548c\uff1a\u3002\u56e0\u6b64\uff0c\u53ef\u4ee5\u636e\u6b64\u76f4\u63a5\u8fdb\u884c\u6ce2\u5f62\u91cd\u6784\u3002\u5373\u901a\u8fc7FFT\u5f97\u5230\u4fe1\u53f7\u7684\u8c10\u6ce2\u632f\u5e45\u548c\u76f8\u4f4d\u89d2\uff0c\u6309\u7167\u6b64\u5f0f\u91cd\u6784\u4e00\u4e2a\u5e73\u6ed1\u7684\u6ce2\u578b\uff0c\u518d\u62ff\u53bb\u505a\u5fae\u5206\u3002\u539f\u7406\u5f88\u7b80\u5355\uff0c\u4f46\u662f\u5728MATLAB\u91cc\u6574\u4e86\u534a\u5929\uff0c\u5f3a\u5ea6\u662f\u5bf9\u7684\uff0c\u4f46\u76f8\u4f4d\u89d2\u6c38\u8fdc\u662f\u9519\u7684\u3002\u7814\u7a76\u4e86\u4e00\u665a\u4e0a\uff0c\u624d\u53d1\u73b0FFT\u5f97\u5230\u7684\u76f8\u4f4d\u89d2\u603b\u662f\u5c11\u4e8690\u00b0\uff0c\u4e5f\u4e0d\u77e5\u9053\u4ec0\u4e48\u539f\u56e0\u3002\u603b\u4e4b\u52a0\u4e0a\u8fd990\u00b0\u4e4b\u540e\u5c31\u5b8c\u7f8e\u4e86\u3002\u4e3a\u4e86\u51cf\u5c11\u65e5\u540e\u6478\u7d22\uff0c\u628a\u4ee3\u7801\u8d34\u5728\u8fd9\u91cc\uff1a clear all;close all;clc; %============ Generate the signal for reconstruction ============% fs=57; % sampling frequency fi0=10\/3; % input frequency t=0:1\/fs:123456\/fs; % the length of signal is 12345. t=t'; delta=[1 3 2 1]; x1=sin(2*pi*fi0*t); % the input signal is a sinusoidal wave; x2=12*sin(2*pi*fi0*t+1) +3*sin(3*2*pi*fi0*t+3)+0.8*sin(5*2*pi*fi0*t+2)+0.02*sin(7*2*pi*fi0*t+1) +2*rand(size(t)); % the output is a sum\u2026","rel":"","context":"In "\u4ee5tag\u5206\u7c7b\u7684\u6587\u7ae0"","block_context":{"text":"\u4ee5tag\u5206\u7c7b\u7684\u6587\u7ae0","link":"https:\/\/www.andrewsun.net\/panta_rhei\/archives\/category\/tagged"},"img":{"alt_text":"\u5b9e\u9645\u4fe1\u53f7\u793a\u8303","src":"https:\/\/i0.wp.com\/www.andrewsun.net\/panta_rhei\/wp-content\/uploads\/2012\/05\/Untitled1.png?resize=350%2C200","width":350,"height":200,"srcset":"https:\/\/i0.wp.com\/www.andrewsun.net\/panta_rhei\/wp-content\/uploads\/2012\/05\/Untitled1.png?resize=350%2C200 1x, 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1.5x"},"classes":[]},{"id":1031,"url":"https:\/\/www.andrewsun.net\/panta_rhei\/archives\/1031","url_meta":{"origin":2903,"position":2},"title":"\u4e3a\u4ec0\u4e48G''\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 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)[\/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 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"\u8bc4\u8bba"","block_context":{"text":"\u8bc4\u8bba","link":"https:\/\/www.andrewsun.net\/panta_rhei\/archives\/category\/personal\/%e8%af%84%e8%ae%ba"},"img":{"alt_text":"","src":"","width":0,"height":0},"classes":[]},{"id":5244,"url":"https:\/\/www.andrewsun.net\/panta_rhei\/archives\/5244","url_meta":{"origin":2903,"position":4},"title":"Fourier\u53d8\u6362\uff08\u4e00\uff09","author":"Andrew","date":"2013\u5e744\u67088\u65e5","format":false,"excerpt":"[mathjax] \u4e3a\u4e86\u5e26\u5e08\u5f1f\u505a\u5b9e\u9a8c\uff0c\u7b80\u8981\u603b\u7ed3\u4e00\u4e0b\u5728MATLAB\u91cc\u8fdb\u884cFourier\u53d8\u6362\u7684\u4e00\u4e9b\u4ee3\u7801\uff0c\u4ee5\u4f9b\u5927\u5bb6\u53c2\u8003\u3002 Discrete Fourier transform (DFT): The sequence of N complex numbers x0, ..., xN-1 is transformed into an N-periodic sequence of complex numbers according to the DFT formula . \u4e00\u822c\u628a\u53d8\u6362\u524d\u7684\u4fe1\u53f7xn\u5f53\u6210\u65f6\u57df\u4fe1\u53f7\uff0c\u53d8\u6362\u540e\u7684Xk\u5f53\u6210\u9891\u57df\u4fe1\u53f7\u3002\u53ef\u89c1\uff0c\u65f6\u57df\u662fN\u4e2a\u5355\u5143\u7684\u4fe1\u53f7\uff0c\u53d8\u6362\u540e\u9891\u57df\u8fd8\u662fN\u4e2a\u5355\u5143\u7684\u4fe1\u53f7\u3002\u4ec0\u4e48\u5468\u671f\u554a\u9891\u7387\u554a\u8fd9\u4e9b\u4fe1\u606f\u662f\u6682\u65f6\u6ca1\u6709\u7684\u3002\u4f8b\u5982xn\u4e3a\u4ee5\u4e0b\u8fd9\u4e2a\u5e8f\u5217\uff08Fig. 1\uff09\uff0c\u6a2a\u5750\u6807\u5c31\u662f\u5e8f\u53f7n\u3002\u8fd9\u6bb5\u5e8f\u5217\uff0c\u53ef\u4ee5\u662f\u4e00\u6bb510\u79d2\u949f\u7684\u7684\u4fe1\u53f7\uff0c\u4e5f\u53ef\u4ee5\u662f\u4e00\u6bb5100\u79d2\u949f\u7684\u4fe1\u53f7\u3002\u5f53\u7136\uff0c\u5b9e\u9645\u60c5\u51b5\u4e0b\u4e00\u6bb5\u4fe1\u53f7\u662f\u591a\u5c11\u79d2\u662f\u4e8b\u5148\u77e5\u9053\u7684\uff0c\u51fa\u6765\u7684\u4fe1\u53f7\u4e00\u5171\u6709\u591a\u5c11\u4e2a\u5355\u5143\u503c\uff08N\uff09\u5219\u53d6\u51b3\u4e8e\u6211\u4eec\u9694\u591a\u957f\u65f6\u95f4\u53d6\u4e00\u6b21\u6837\u3002\u5982\u679c\u4e00\u6bb510\u79d2\u949f\u7684\u4fe1\u53f7\uff0c\u6211\u4eec\u6bcf\u79d2\u53d6\u4e00\u6b21\u6837\uff0c\u8fd9\u4e2a\u5e8f\u5217\u5c31\u670910\u4e2a\u5355\u5143\uff08N = 10\uff09\u3002\u53cd\u4e4b\uff0cFig. 1\u7684\u8fd9\u4e2a\u5e8f\u5217N = 93\uff0c\u5047\u5982\u8fd9\u4e2a\u4fe1\u53f7\u662f\u6bcf\u96940.1\u79d2\u53d6\u4e00\u6b21\u6837\u5f97\u5230\u7684\uff0c\u8fd9\u4e2a\u4fe1\u53f7\u7684\u603b\u65f6\u957f\u5c31\u662f9.2\u79d2\uff1b\u800c\u5047\u5982\u8fd9\u4e2a\u4fe1\u53f7\u662f\u6bcf\u969410\u79d2\u53d6\u4e00\u6b21\u6837\u5f97\u5230\u7684\uff0c\u8fd9\u4e2a\u4fe1\u53f7\u603b\u65f6\u957f\u5c31\u662f920\u79d2\u4e86\u3002\u6bcf\u9694\u591a\u957f\u65f6\u95f4\u53d6\u4e00\u6b21\u6837\uff0c\u53ef\u4ee5\u7528\u53d6\u6837\u9891\u7387fs\u6765\u8868\u793a\u3002fs = 10 Hz\u5c31\u662f\u6bcf\u96940.1 s\u53d6\u4e00\u6b21\u6837\u3002\u6240\u4ee5\uff0c\u4e3a\u4e86\u7ed9\u4e00\u5bf9\u79bb\u6563Fourier\u53d8\u6362xn\u548cXk\u8d4b\u4ee5\u5468\u671f\u6216\u9891\u7387\u7684\u4fe1\u606f\uff0c\u5fc5\u987b\u7ed9\u65f6\u57df\u4fe1\u53f7\u89c4\u5b9a\u4e00\u4e2afs\u3002\u4e00\u65e6fs\u89c4\u5b9a\u4e86\uff0c\u5468\u671f\u548c\u9891\u7387\u4e5f\u5c31\u89c4\u5b9a\u4e86\u3002\u8fd8\u62ffFig. 1\u7684\u5e8f\u5217\u4e3a\u4f8b\uff0c\u8bbe\u8be5\u5e8f\u5217\u7684\u53d6\u6837\u9891\u7387fs = 10 Hz\uff0c\u5219\u8be5\u5e8f\u5217\u6bcf\u4e2a\u5355\u5143\u9694\u4e860.1 s\u3002\u6211\u4eec\u53ef\u4ee5\u6570\u4e00\u4e0b\u8fd9\u4e2a\u5e8f\u5217\u4e00\u4e2a\u5468\u671f\u6709\u591a\u5c11\u4e2a\u5355\u5143\u2014\u201420\u4e2a\uff0c\u90a3\u4e48\u8be5\u5e8f\u5217\u7684\u5468\u671fT = 2 s\uff0c\u9891\u7387f =\u2026","rel":"","context":"In "\u5de5\u4f5c\u7b14\u8bb0"","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","src":"https:\/\/i0.wp.com\/www.andrewsun.net\/panta_rhei\/wp-content\/uploads\/2013\/04\/f1.png?resize=350%2C200","width":350,"height":200,"srcset":"https:\/\/i0.wp.com\/www.andrewsun.net\/panta_rhei\/wp-content\/uploads\/2013\/04\/f1.png?resize=350%2C200 1x, 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