{"id":291400,"date":"2023-07-04T07:18:37","date_gmt":"2023-07-04T07:18:37","guid":{"rendered":"\/forum\/forums\/topic\/problem-about-euler-beam\/"},"modified":"2023-07-07T07:38:00","modified_gmt":"2023-07-07T07:38:00","slug":"problem-about-euler-beam","status":"closed","type":"topic","link":"https:\/\/innovationspace.ansys.com\/forum\/forums\/topic\/problem-about-euler-beam\/","title":{"rendered":"Problem about Euler beam"},"content":{"rendered":"

Hello, I’m leaving a post because I have a question while solving a simple cantliever beam problem. The problem is that the natural frequency calculated at Ansys is less than the theoretical value.<\/p>\n

I learned Euler’s beam theory, and I was able to get a characteristic equation of a beam that was fixed at one end and free at the other.<\/p>\n

< cos(beta*L)*cosh(beta*L)=-1 ><\/p>\n

Calculated using the Newton-Raphson method, the value of beta*L was obtained as follows.<\/p>\n

< beta1*L=1.8751 >, < beta2*L=4.6941 >, < beta3*L=7.8547575 > ….<\/p>\n

When the following properties are applied, the natural frequency value is calculated as follows.<\/p>\n

< Properties, Structural Steel: Young’s modulus of 200 GPa and density of 7850 kg\/m^3<\/span><\/p>\n

Cross-Section: Rectangular, Length: 0.3m, Wide: 0.03m and Thickness: 0.005m ><\/p>\n

Natural frequencies: <45.2987>, <283.8846>, <794.8821>, ….<\/p>\n

 <\/p>\n

Ansys model results using beam4 (Number of elements: 40)<\/p>\n

Natural frequecies: <45.296>, <283.78>, <794.17>, …<\/p>\n

 <\/p>\n

I learned in class that the exact solution at the natural frequency is always the same or less than the approximation. Ansys calculates using approximate solutions, so it must be less than exact solution, so I wonder why this is the result.<\/div>\n
 <\/div>\n
Are there any additional tools that are reflected on the Ansys? This difference is confirmed that the error increases as the thickness of the beam increases, and the above result is a small difference.<\/div>\n
 <\/div>\n
cf) Additionally, I wonder if Ansys uses Timoshenko Beam theory for the basic analysis setting of beam modeling.<\/div>\n

 <\/p>\n

Thank you<\/p>\n","protected":false},"template":"","class_list":["post-291400","topic","type-topic","status-closed","hentry"],"aioseo_notices":[],"acf":[],"custom_fields":[{"0":{"_bbp_subscription":["288588","13640"],"_bbp_author_ip":["168.143.243.14"]," _bbp_last_reply_id":["0"]," _bbp_likes_count":["0"],"_btv_view_count":["389"],"_edit_lock":["1688715404:222993"],"_bbp_likes_count":["1"],"_bbp_topic_status":["unanswered"],"_bbp_status":["publish"],"_bbp_topic_id":["291400"],"_bbp_forum_id":["27791"],"_bbp_engagement":["13640","288588"],"_bbp_voice_count":["2"],"_bbp_reply_count":["2"],"_bbp_last_reply_id":["292007"],"_bbp_last_active_id":["292007"],"_bbp_last_active_time":["2023-07-07 07:43:40"]},"test":"dksdygks02hanyang-ac-kr"}],"_links":{"self":[{"href":"https:\/\/innovationspace.ansys.com\/forum\/wp-json\/wp\/v2\/topics\/291400","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\/291400\/revisions"}],"wp:attachment":[{"href":"https:\/\/innovationspace.ansys.com\/forum\/wp-json\/wp\/v2\/media?parent=291400"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}