{"id":313752,"date":"2023-10-28T10:05:21","date_gmt":"2023-10-28T10:05:21","guid":{"rendered":"\/forum\/forums\/topic\/apdl-math-example-4-1verify-orthogonality-of-eigenmodes-after-a-modal-analysis\/"},"modified":"2023-11-04T09:01:52","modified_gmt":"2023-11-04T09:01:52","slug":"apdl-math-example-4-1verify-orthogonality-of-eigenmodes-after-a-modal-analysis","status":"closed","type":"topic","link":"https:\/\/innovationspace.ansys.com\/forum\/forums\/topic\/apdl-math-example-4-1verify-orthogonality-of-eigenmodes-after-a-modal-analysis\/","title":{"rendered":"APDL Math Example 4.1&#8243;Verify Orthogonality of Eigenmodes after a Modal Analysis"},"content":{"rendered":"<p style=\"color: #252525\">Hello everyone,<\/p>\n<p style=\"color: #252525\">In an older post, I was asking about some methods to extract the eigenvectors of modal analysis in order to proceed with further analysis, such as orthogonality checks and the modal assurance criterion (MAC) for this modal analysis. Gratefully, some fellows showed me the example in the title. In this example, check orthogonality by multiplying the (transpose of the modal matrix*mass matrix*modal matrix) to receive the dentity matrix !!<\/p>\n<p style=\"color: #252525\">In the text books, the orthogonality check for two vectors is done by the dot product of those two vectors; if they are orthogonal, then their dot multiplication should be equal to zero. when I tried to do this with the vectors of (SOLVPhi) in the shown example, but unfortunately it didn&#8217;t fulfill the condition of the orthogonality, which should (according to text books) be zero.<\/p>\n<p style=\"color: #252525\">Also, it will be greatly appreciated if there is any way to use MAC for these eigenvectors.<\/p>\n<p style=\"color: #252525\">Regards.<\/p>\n","protected":false},"template":"","class_list":["post-313752","topic","type-topic","status-closed","hentry","topic-tag-Modal_Analysis-1","topic-tag-apdl","topic-tag-eigenmode","topic-tag-orthogonality-1"],"aioseo_notices":[],"acf":[],"custom_fields":[{"0":{"_bbp_subscription":["51194","18229"],"_bbp_author_ip":["96.7.218.215"]," _bbp_last_reply_id":["0"]," _bbp_likes_count":["0"],"_btv_view_count":["1425"],"_edit_lock":["1698498859:117528"],"_bbp_status":["publish"],"_bbp_topic_status":["unanswered"],"_bbp_topic_id":["313752"],"_bbp_forum_id":["27791"],"_bbp_engagement":["18229","51194"],"_bbp_voice_count":["2"],"_bbp_reply_count":["3"],"_bbp_last_reply_id":["314238"],"_bbp_last_active_id":["314238"],"_bbp_last_active_time":["2023-11-01 00:20:18"]},"test":"md_abdelrhimhotmail-com"}],"_links":{"self":[{"href":"https:\/\/innovationspace.ansys.com\/forum\/wp-json\/wp\/v2\/topics\/313752","targetHints":{"allow":["GET"]}}],"collection":[{"href":"https:\/\/innovationspace.ansys.com\/forum\/wp-json\/wp\/v2\/topics"}],"about":[{"href":"https:\/\/innovationspace.ansys.com\/forum\/wp-json\/wp\/v2\/types\/topic"}],"version-history":[{"count":0,"href":"https:\/\/innovationspace.ansys.com\/forum\/wp-json\/wp\/v2\/topics\/313752\/revisions"}],"wp:attachment":[{"href":"https:\/\/innovationspace.ansys.com\/forum\/wp-json\/wp\/v2\/media?parent=313752"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}