{"id":10716,"date":"2018-12-25T10:35:37","date_gmt":"2018-12-25T02:35:37","guid":{"rendered":"http:\/\/www.jdcui.com\/?p=10716"},"modified":"2026-02-17T09:20:10","modified_gmt":"2026-02-17T01:20:10","slug":"%e5%8a%a8%e5%8a%9b%e5%ad%a6-%e6%a8%a1%e6%80%81%e5%88%86%e6%9e%90%e5%9f%ba%e7%a1%80-basics-of-modal-analysis","status":"publish","type":"post","link":"http:\/\/www.jdcui.com\/?p=10716","title":{"rendered":"[\u52a8\u529b\u5b66] \u6a21\u6001\u5206\u6790\u57fa\u7840 (Basics of Modal Analysis) (\u300a\u6709\u9650\u5355\u5143\u6cd5-\u7f16\u7a0b\u4e0e\u8f6f\u4ef6\u5e94\u7528\u300b\u7ae0\u8282\u8282\u9009)"},"content":{"rendered":"<p><span style=\"color: #ff00ff;\"><strong>\u5b9e\u5e72\u3001\u5b9e\u8df5\u3001\u79ef\u7d2f\u3001\u601d\u8003\u3001\u521b\u65b0\u3002<\/strong><\/span><\/p>\n<p><!--more--><\/p>\n<p><a href=\"http:\/\/www.jdcui.com\/?page_id=9731\" target=\"_blank\" rel=\"noopener\"><strong>\u300a\u6709\u9650\u5355\u5143\u6cd5\uff1a\u7f16\u7a0b\u4e0e\u8f6f\u4ef6\u5e94\u7528\u300b<\/strong><\/a>\u6a21\u6001\u5206\u6790\u7ae0\u8282\u7684\u5185\u5bb9\u8282\u9009\uff1a<\/p>\n<p>\u6a21\u6001\u5206\u6790\u662f\u4e00\u79cd\u7814\u7a76\u7ed3\u6784\u52a8\u529b\u7279\u6027\u7684\u65b9\u6cd5\uff0c\u901a\u8fc7\u6a21\u6001\u5206\u6790\uff0c\u53ef\u4ee5\u5f97\u5230\u7ed3\u6784\u5404\u9636\u6a21\u6001\u7684\u9891\u7387\u548c\u632f\u578b\u3002\u5728\u7ed3\u6784\u5de5\u7a0b\u4e2d\uff0c\u6a21\u6001\u5206\u6790\u662f\u8fdb\u884c\u7ed3\u6784\u52a8\u529b\u5206\u6790\u548c\u6297\u9707\u8bbe\u8ba1\u7684\u57fa\u7840\uff0c\u98ce\u8377\u8f7d\u8ba1\u7b97\u65f6\uff0c\u4e5f\u5e38\u5e38\u9700\u8981\u6a21\u6001\u5206\u6790\u63d0\u4f9b\u7684\u5468\u671f\u53c2\u6570\u3002\u672c\u7ae0\u9996\u5148\u7b80\u8981\u4ecb\u7ecd\u6a21\u6001\u5206\u6790\u7684\u57fa\u672c\u539f\u7406\uff0c\u7136\u540e\u4ee5\u4e00\u4e2a\u6841\u67b6\u7ed3\u6784\u548c\u4e00\u4e2a\u6846\u67b6\u7ed3\u6784\u4e3a\u4f8b\uff0c\u4ecb\u7ecd\u6709\u9650\u5143\u6cd5\u8fdb\u884c\u6a21\u6001\u5206\u6790\u7684\u7f16\u7a0b\u8fc7\u7a0b\u53ca\u5176\u5728\u5177\u4f53\u8f6f\u4ef6\u4e2d\u7684\u5e94\u7528\u3002<\/p>\n<ul style=\"list-style-type: square;\">\n<li><span style=\"color: #0000ff;\">\u57fa\u672c\u65b9\u7a0b<\/span><\/li>\n<\/ul>\n<p>\u6839\u636e\u7ed3\u6784\u52a8\u529b\u5b66\u77e5\u8bc6\uff0c\u4f53\u7cfb\u65e0\u963b\u5c3c\u81ea\u7531\u632f\u52a8\u65b9\u7a0b\u4e3a<\/p>\n<p style=\"text-align: center;\"><img loading=\"lazy\" decoding=\"async\" class=\"wp-image-10740 alignnone\" src=\"http:\/\/www.jdcui.com\/wp-content\/uploads\/2018\/12\/ModalAnalysis_E10_1_1.png\" alt=\"\" width=\"180\" height=\"42\" srcset=\"http:\/\/www.jdcui.com\/wp-content\/uploads\/2018\/12\/ModalAnalysis_E10_1_1.png 308w, http:\/\/www.jdcui.com\/wp-content\/uploads\/2018\/12\/ModalAnalysis_E10_1_1-300x71.png 300w\" sizes=\"auto, (max-width: 180px) 100vw, 180px\" \/>\u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0(10.1\u20111)<\/p>\n<p>\u5176\u4e2d\u00a0<strong>[M]<\/strong>\u548c\u00a0<strong>[K]<\/strong>\u5206\u522b\u4e3a\u7ed3\u6784\u7684\u8d28\u91cf\u77e9\u9635\u53ca\u521a\u5ea6\u77e9\u9635\uff0c <img loading=\"lazy\" decoding=\"async\" class=\" wp-image-10741 alignnone\" src=\"http:\/\/www.jdcui.com\/wp-content\/uploads\/2018\/12\/ModalAnalysis_ACC.png\" alt=\"\" width=\"32\" height=\"38\" \/>\u548c <img loading=\"lazy\" decoding=\"async\" class=\"size-full wp-image-10742 alignnone\" src=\"http:\/\/www.jdcui.com\/wp-content\/uploads\/2018\/12\/ModalAnalysis_DISP.png\" alt=\"\" width=\"29\" height=\"31\" \/>\u00a0\u5206\u522b\u4e3a\u7ed3\u6784\u7684\u8282\u70b9\u4f4d\u79fb\u53ca\u8282\u70b9\u52a0\u901f\u5ea6\u5217\u9635\uff0c\u4e0a\u5f0f\u662f\u4e00\u4e2a\u5e38\u7cfb\u6570\u9f50\u6b21\u7ebf\u6027\u5fae\u5206\u65b9\u7a0b\u7ec4\uff0c\u5176\u89e3\u7684\u5f62\u5f0f\u4e3a<\/p>\n<p style=\"text-align: center;\"><img loading=\"lazy\" decoding=\"async\" class=\"size-full wp-image-10743 alignnone\" src=\"http:\/\/www.jdcui.com\/wp-content\/uploads\/2018\/12\/ModalAnalysis_E10_2_1.png\" alt=\"\" width=\"138\" height=\"37\" \/>\u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0(10.1\u20112)<\/p>\n<p>\u5176\u4e2d <img loading=\"lazy\" decoding=\"async\" class=\"size-full wp-image-10744 alignnone\" src=\"http:\/\/www.jdcui.com\/wp-content\/uploads\/2018\/12\/ModalAnalysis_DISP0.png\" alt=\"\" width=\"33\" height=\"34\" \/>\u00a0\u4e0e\u65f6\u95f4\u65e0\u5173\u3002\u5c06\u65b9\u7a0b\u89e3(10.1\u20112) \u5e26\u5165\u65b9\u7a0b(10.1\u20111)\uff0c\u53ef\u5f97<\/p>\n<p style=\"text-align: center;\"><img loading=\"lazy\" decoding=\"async\" class=\"size-full wp-image-10745 alignnone\" src=\"http:\/\/www.jdcui.com\/wp-content\/uploads\/2018\/12\/ModalAnalysis_E10_3_1.png\" alt=\"\" width=\"204\" height=\"36\" \/>\u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 (10.1\u20113)<\/p>\n<p>\u4e0a\u5f0f\u662f\u9f50\u6b21\u7ebf\u6027\u4ee3\u6570\u65b9\u7a0b\u7ec4\uff0c\u5176\u6709\u975e\u96f6\u89e3\u7684\u6761\u4ef6\u662f\u7cfb\u6570\u884c\u5217\u5f0f\u7b49\u4e8e\u96f6\uff0c\u5373<\/p>\n<p style=\"text-align: center;\">\u00a0 \u00a0 \u00a0 \u00a0<img loading=\"lazy\" decoding=\"async\" class=\"size-full wp-image-10747 alignnone\" src=\"http:\/\/www.jdcui.com\/wp-content\/uploads\/2018\/12\/ModalAnalysis_E10_4_1.png\" alt=\"\" width=\"157\" height=\"41\" \/>\u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 (10.1\u20114)<\/p>\n<p>\u5982\u679c\u00a0<strong>[K]\u00a0<\/strong>\u548c\u00a0<strong>[M]<\/strong>\u7684\u9636\u6570\u4e3an\uff0c\u5219(10.1\u20114)\u662f \u7684n\u6b21\u65b9\u7a0b\uff0c\u79f0\u4f5c\u7ed3\u6784\u81ea\u7531\u632f\u52a8\u7279\u5f81\u65b9\u7a0b\u3002 \u79f0\u4e3a\u7279\u5f81\u503c\u3002\u5c06\u7279\u5f81\u503c\u5e26\u5165(10.1\u20113)\uff0c\u53ef\u6c42\u5f97\u76f8\u5e94\u7684<img loading=\"lazy\" decoding=\"async\" class=\"size-full wp-image-10744 alignnone\" src=\"http:\/\/www.jdcui.com\/wp-content\/uploads\/2018\/12\/ModalAnalysis_DISP0.png\" alt=\"\" width=\"33\" height=\"34\" \/> \uff0c\u79f0\u4e3a\u7279\u5f81\u5411\u91cf\u3002\u7b2ci\u4e2a<strong><em>w<\/em><sub>i<\/sub><sup>2<\/sup><\/strong> \u3001<img loading=\"lazy\" decoding=\"async\" class=\"size-full wp-image-10746 alignnone\" src=\"http:\/\/www.jdcui.com\/wp-content\/uploads\/2018\/12\/ModalAnalysis_DISP0i.png\" alt=\"\" width=\"40\" height=\"33\" \/> \u79f0\u4e3a\u7b2ci\u7279\u5f81\u5bf9\u3002 <strong><em>w<\/em><sub>i<\/sub><\/strong>\u5373\u7ed3\u6784\u7b2ci\u4e2a\u56fa\u6709\u9891\u7387\uff0c<img loading=\"lazy\" decoding=\"async\" class=\"size-full wp-image-10746 alignnone\" src=\"http:\/\/www.jdcui.com\/wp-content\/uploads\/2018\/12\/ModalAnalysis_DISP0i.png\" alt=\"\" width=\"40\" height=\"33\" \/> \u5373\u7ed3\u6784\u7b2ci\u4e2a\u632f\u578b\u3002<\/p>\n<ul style=\"list-style-type: square;\">\n<li><span style=\"color: #0000ff;\">\u6c42\u89e3\u65b9\u6cd5<\/span><\/li>\n<\/ul>\n<p>\u516c\u5f0f(10.1\u20113)\u5728\u6570\u5b66\u4e0a\u79f0\u4e3a<span style=\"color: #ff00ff;\"><strong>\u5e7f\u4e49\u7279\u5f81\u503c<\/strong><\/span>\u95ee\u9898\uff0c\u4e00\u822c\u8bb0\u4f5c<\/p>\n<p style=\"text-align: center;\">\u00a0 \u00a0 \u00a0<img loading=\"lazy\" decoding=\"async\" class=\"size-full wp-image-10748 alignnone\" src=\"http:\/\/www.jdcui.com\/wp-content\/uploads\/2018\/12\/ModalAnalysis_E10_5_1.png\" alt=\"\" width=\"185\" height=\"38\" \/>\u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0(10.1\u20115)<\/p>\n<p>\u901a\u5e38\u6709\u4e24\u79cd\u65b9\u6cd5\u6c42\u89e3\u65b9\u7a0b\u3002\u4e00\u662f\u6309\u6c42\u5e7f\u4e49\u7279\u5f81\u503c\u95ee\u9898\u7684\u76f8\u5e94\u65b9\u6cd5\u6c42\u89e3\uff0c\u4f8b\u5982\u5e7f\u4e49\u96c5\u514b\u6bd4\u6cd5\u3001\u5b50\u7a7a\u95f4\u8fed\u4ee3\u6cd5\uff1b\u4e8c\u662f\u5148\u5c06\u4e0a\u5f0f\u53d8\u6362\u4e3a\u6807\u51c6\u7279\u5f81\u503c\u95ee\u9898\uff0c\u518d\u6309\u76f8\u5e94\u7684\u65b9\u6cd5\u6c42\u89e3\u3002\u672c\u4f8b\u91c7\u7528\u540e\u8005\u3002<\/p>\n<p>\u6807\u51c6\u7279\u5f81\u503c\u95ee\u9898\u7684\u516c\u5f0f\u8868\u793a\u4e3a<\/p>\n<p style=\"text-align: center;\">\u00a0 \u00a0 <img loading=\"lazy\" decoding=\"async\" class=\"size-full wp-image-10749 alignnone\" src=\"http:\/\/www.jdcui.com\/wp-content\/uploads\/2018\/12\/ModalAnalysis_E10_6_1.png\" alt=\"\" width=\"138\" height=\"34\" \/>\u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0(10.1\u20116)<\/p>\n<p>\u5bf9\u4e8e(10.1\u20115),<strong>\u82e5\u00a0[M]<sup>-1<\/sup><\/strong> \u5b58\u5728\uff0c\u5219\u516c\u5f0f\u53d8\u4e3a<\/p>\n<p style=\"text-align: center;\">\u00a0 \u00a0 \u00a0 \u00a0 \u00a0<img loading=\"lazy\" decoding=\"async\" class=\"size-full wp-image-10750 alignnone\" src=\"http:\/\/www.jdcui.com\/wp-content\/uploads\/2018\/12\/ModalAnalysis_E10_7_1.png\" alt=\"\" width=\"206\" height=\"32\" \/>\u00a0 \u00a0 \u00a0 \u00a0 \u00a0(10.1\u20117)<\/p>\n<p>\u5373 <img loading=\"lazy\" decoding=\"async\" class=\"size-full wp-image-10751 alignnone\" src=\"http:\/\/www.jdcui.com\/wp-content\/uploads\/2018\/12\/ModalAnalysis_A.png\" alt=\"\" width=\"207\" height=\"35\" \/>\u3002<\/p>\n<p><strong>\u82e5<\/strong> <strong>[K]<sup>-1<\/sup><\/strong>\u5b58\u5728\uff0c\u5219\u516c\u5f0f\u53d8\u4e3a<\/p>\n<p style=\"text-align: center;\"><img loading=\"lazy\" decoding=\"async\" class=\"size-full wp-image-10753 alignnone\" src=\"http:\/\/www.jdcui.com\/wp-content\/uploads\/2018\/12\/ModalAnalysis_E10_8_1.png\" alt=\"\" width=\"208\" height=\"51\" \/>\u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 (10.1\u20118)<\/p>\n<p>\u5373<img loading=\"lazy\" decoding=\"async\" class=\"size-full wp-image-10754 alignnone\" src=\"http:\/\/www.jdcui.com\/wp-content\/uploads\/2018\/12\/ModalAnalysis_A2.png\" alt=\"\" width=\"211\" height=\"51\" \/>\u00a0 \u3002<\/p>\n<p>\u6c42\u5f97\u7279\u5f81\u503c\u03bb\u540e\uff0c\u53ef\u5e26\u5165\u65b9\u7a0b(10.1\u20116)\u6c42\u5f97\u76f8\u5e94\u7684\u7279\u5f81\u5411\u91cf\u3002<\/p>\n<ul style=\"list-style-type: square;\">\n<li><strong><span style=\"color: #000000;\">\u76f8\u5173\u5185\u5bb9<\/span>\u00a0<span style=\"color: #0000ff;\">( Related Topics )<\/span><\/strong><\/li>\n<\/ul>\n<p><strong><span style=\"color: #000000;\">[00].<\/span><em><span style=\"color: #ff00ff;\">\u00a0<a style=\"color: #ff00ff;\" href=\"http:\/\/www.jdcui.com\/?page_id=9731\" target=\"_blank\" rel=\"noopener\">[Book][\u4e66] \u6709\u9650\u5355\u5143\u6cd5\uff1a\u7f16\u7a0b\u4e0e\u8f6f\u4ef6\u5e94\u7528<\/a><\/span><\/em><\/strong><\/p>\n<p><strong><span style=\"color: #000000;\">[01].<\/span>\u00a0<a href=\"http:\/\/www.jdcui.com\/?p=1927\">2D Truss by Matlab [Matlab 2D\u6841\u67b6\u6709\u9650\u5143] (code by myself)<\/a><\/strong><\/p>\n<p><strong><span style=\"color: #000000;\">[02].<\/span>\u00a0<a href=\"http:\/\/www.jdcui.com\/?p=1945\">3D Truss by MATLAB[MATLAB 3D \u6841\u67b6\u9759\u529b\u5206\u6790] (code by myself)<\/a><\/strong><\/p>\n<p><strong><span style=\"color: #000000;\">[03].<\/span>\u00a0<a href=\"http:\/\/www.jdcui.com\/?p=8767\">[FEM][\u6709\u9650\u5143][\u7f16\u7a0b][Matlab][Code by myself] FEM Analysis: 2D Truss Element [\u6709\u9650\u5143\u5206\u6790: 2D\u6841\u67b6\u5355\u5143]<\/a><\/strong><\/p>\n<p><strong><span style=\"color: #000000;\">[04].<\/span>\u00a0<a href=\"http:\/\/www.jdcui.com\/?p=8778\">[FEM][\u6709\u9650\u5143][\u7f16\u7a0b][Matlab][Code by myself] FEM Analysis: 2D Euler Beam Element [\u6709\u9650\u5143\u5206\u6790: 2D\u6b27\u62c9\u6881\u5355\u5143]<\/a><\/strong><\/p>\n<p><strong><span style=\"color: #000000;\">[05].<\/span>\u00a0<a href=\"http:\/\/www.jdcui.com\/?p=8955\">[FEM][\u6709\u9650\u5143][\u7f16\u7a0b][Matlab][Code by myself] 2D\u526a\u5207\u6881\u5355\u5143<\/a><\/strong><\/p>\n<p><strong><span style=\"color: #000000;\">[06].<\/span>\u00a0<a href=\"http:\/\/www.jdcui.com\/?p=8977\">[FEM][\u6709\u9650\u5143][\u7f16\u7a0b][Matlab][Code by myself] 2D Timoshenko\u6881\u5355\u5143<\/a><\/strong><\/p>\n<p><strong><span style=\"color: #000000;\">[07].<\/span>\u00a0<a href=\"http:\/\/www.jdcui.com\/?p=8988\">[FEM][\u6709\u9650\u5143][\u7f16\u7a0b][Matlab][Code by myself] \u4e09\u89d2\u5f62\u5e38\u5e94\u53d8\u5355\u5143(CST)<\/a><\/strong><\/p>\n<p><strong><span style=\"color: #000000;\">[08].<\/span>\u00a0<a href=\"http:\/\/www.jdcui.com\/?p=8991\">[FEM][\u6709\u9650\u5143][\u7f16\u7a0b][Matlab][Code by myself] \u5e73\u97624\u53d8\u5f62\u5355\u5143(Q4)<\/a><\/strong><\/p>\n<p><strong><span style=\"color: #000000;\">[09].<\/span>\u00a0<a href=\"http:\/\/www.jdcui.com\/?p=8999\">[FEM][\u6709\u9650\u5143][\u7f16\u7a0b][Matlab][Code by myself] 4\u8282\u70b9\u56db\u9762\u4f53\u5355\u5143(TET4)<\/a><\/strong><\/p>\n<p><strong><span style=\"color: #000000;\">[10].<\/span>\u00a0<a href=\"http:\/\/www.jdcui.com\/?p=9012\">[FEM][\u6709\u9650\u5143][\u7f16\u7a0b][Matlab][Code by myself] 8\u8282\u70b9\u516d\u9762\u4f53\u5355\u5143(C3D8)<\/a><\/strong><\/p>\n<p><strong><span style=\"color: #000000;\">[11].<\/span>\u00a0<a href=\"http:\/\/www.jdcui.com\/?p=9087\">[FEM][\u6709\u9650\u5143][\u7f16\u7a0b][Matlab][Code by myself] \u5e73\u97628\u8282\u70b9\u4e8c\u6b21\u201c\u5b8c\u5168\u79ef\u5206\u201d\u5355\u5143(CPS8)<\/a><\/strong><\/p>\n<p><strong><span style=\"color: #000000;\">[12].<\/span>\u00a0<a href=\"http:\/\/www.jdcui.com\/?p=9115\">[FEM][\u6709\u9650\u5143][\u7f16\u7a0b][Matlab][Code by myself] \u5e73\u97626\u8282\u70b9\u4e8c\u6b21\u201c\u5b8c\u5168\u79ef\u5206\u201d\u5355\u5143(CPS6)<\/a><\/strong><\/p>\n<p><strong><span style=\"color: #000000;\">[13].<\/span>\u00a0<a href=\"http:\/\/www.jdcui.com\/?p=10718\">[FEM][MATLAB][\u6709\u9650\u5143] FEM Modal Analysis Programming with MATLAB (Truss Element) (\u6841\u67b6\u5355\u5143\u6a21\u6001\u5206\u6790\u7f16\u7a0b)<\/a><\/strong><\/p>\n<p><strong><span style=\"color: #000000;\">[14].<\/span>\u00a0<a href=\"http:\/\/www.jdcui.com\/?p=10721\">[FEM][MATLAB][\u6709\u9650\u5143] FEM Modal Analysis Programming with MATLAB (Frame Elements) (\u6846\u67b6\u5355\u5143\u6a21\u6001\u5206\u6790\u7f16\u7a0b)<\/a><\/strong><\/p>\n<p><strong><span style=\"color: #000000;\">[15].<\/span>\u00a0<a href=\"http:\/\/www.jdcui.com\/?p=10724\">[\u529b\u5b66][\u6709\u9650\u5143]Basics of Linear Buckling Analysis [\u7ebf\u6027\u66f2\u5c48\u5206\u6790\u57fa\u7840]<\/a><\/strong><\/p>\n<p><strong><span style=\"color: #000000;\">[16].<\/span>\u00a0<a href=\"http:\/\/www.jdcui.com\/?p=10726\">[FEM][MATLAB][\u6709\u9650\u5143][\u7f16\u7a0b] FEM Buckling Analysis Programming with MATLAB (Truss Elements) (\u6841\u67b6\u5355\u5143\u66f2\u5c48\u5206\u6790\u7f16\u7a0b)<\/a><\/strong><\/p>\n<p><strong><span style=\"color: #000000;\">[17].<\/span>\u00a0<a href=\"http:\/\/www.jdcui.com\/?p=10728\">[FEM][MATLAB][\u6709\u9650\u5143][\u7f16\u7a0b] FEM Buckling Analysis Programming with MATLAB (Frame Elements) (\u6846\u67b6\u5355\u5143\u66f2\u5c48\u5206\u6790\u7f16\u7a0b)<\/a><\/strong><\/p>\n<hr \/>\n<p><center><strong><div  class=\"thumbs-rating-container\" id=\"thumbs-rating-10716\" data-content-id=\"10716\"><button class=\"thumbs-rating-up thumbs-rating-voted\" onclick=\"thumbs_rating_vote(10716, 1);\">Vote Up +9<\/button> <button class=\"thumbs-rating-down thumbs-rating-voted\" 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#ff00ff;\">\u7ed3\u6784\u4e4b\u65c5<\/span>\u201d\u00a0\u5fae\u4fe1\u516c\u4f17\u53f7<\/strong><\/p>\n","protected":false},"excerpt":{"rendered":"<p>\u5b9e\u5e72\u3001\u5b9e\u8df5\u3001\u79ef\u7d2f\u3001\u601d\u8003\u3001\u521b\u65b0\u3002<\/p>\n","protected":false},"author":1,"featured_media":10756,"comment_status":"open","ping_status":"open","sticky":false,"template":"","format":"standard","meta":{"footnotes":""},"categories":[382,100,5],"tags":[139,1664,280,443,293,1503,140,1663],"class_list":["post-10716","post","type-post","status-publish","format-standard","has-post-thumbnail","hentry","category-dynamics-","category-fem-","category-structural-engineering","tag-modal-analysis","tag-programming-and-application","tag-280","tag-443","tag-293","tag-1503","tag-140","tag-1663"],"aioseo_notices":[],"aioseo_head":"\n\t\t<!-- All in One SEO 4.9.10 - aioseo.com -->\n\t<meta name=\"robots\" content=\"max-image-preview:large\" \/>\n\t<meta name=\"author\" content=\"CJD\"\/>\n\t<meta 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