{"id":371942,"date":"2024-07-15T14:27:41","date_gmt":"2024-07-15T14:27:41","guid":{"rendered":"https:\/\/innovationspace.ansys.com\/forum\/forums\/topic\/stiffness-calculation-modal-vs-static-structural-analyses\/"},"modified":"2024-07-17T08:44:42","modified_gmt":"2024-07-17T08:44:42","slug":"stiffness-calculation-modal-vs-static-structural-analyses","status":"closed","type":"topic","link":"https:\/\/innovationspace.ansys.com\/forum\/forums\/topic\/stiffness-calculation-modal-vs-static-structural-analyses\/","title":{"rendered":"Stiffness Calculation: Modal vs. Static Structural Analyses"},"content":{"rendered":"

Hi,<\/p>\n

I am having difficulties on correlating the axial stiffness of a simple cube between a modal and a static structural analysis.<\/p>\n

I am analyzing the cube shown below, that has the following properties:<\/p>\n

Cube Length L = 10 mm, Elastic Modulus E = 1050 MPa, Density rho = 7850 kg\/m^3, Normal displacement fixed at one side.<\/p>\n

According to theory, the stiffness is equivalent to K = E A \/ L = 1.05E4 N\/mm, where A = L^2 = 100 mm^2. The axial natural frequency of the cube is then equal to: f = 1\/(2*pi())*sqrt(K\/M), where M is the mass of the cube (0.00785 kg). The axial natural frequency is then calculated as 5821 Hz. However, according to modal analysis results, the axial natural frequency is way higher, f = 8948 Hz.<\/p>\n

For this reason, I have performed a static analysis to check the stiffness of the cube by applying a unit force at one face. The obtained displacement (u = 9.52E-5 mm), confirms an axial stiffness K = F\/u = 1.05E4 N\/mm. Please note that for static analysis convergence, I have fixed the displacement of one vertex on the fixed displacement side.<\/p>\n

Could you please help me understand what I am doing wrong in such a simple simulation?<\/p>\n

Thank you in advance.<\/p>\n

\"\"<\/a><\/span><\/p>\n","protected":false},"template":"","class_list":["post-371942","topic","type-topic","status-closed","hentry","topic-tag-Modal_Analysis-1","topic-tag-natural-frequency","topic-tag-static-structural","topic-tag-stiffness"],"aioseo_notices":[],"acf":[],"custom_fields":[{"0":{"_bbp_subscription":["79564","58821"],"_bbp_author_ip":["93.42.202.76"]," _bbp_last_reply_id":["0"]," _bbp_likes_count":["0"],"_btv_view_count":["2005"],"_bbp_topic_status":["answered"],"_bbp_notification_enabled":["79564","79564","79564","79564","79564","79564"],"_edit_lock":["1721053771:79564"],"_bbp_topic_id":["371942"],"_bbp_forum_id":["27791"],"_bbp_engagement":["58821"],"_bbp_voice_count":["1"],"_bbp_last_reply_id":["372143"],"_bbp_last_active_id":["372143"],"_bbp_last_active_time":["2024-07-16 14:46:14"]},"test":"f-bassiexergy-it"}],"_links":{"self":[{"href":"https:\/\/innovationspace.ansys.com\/forum\/wp-json\/wp\/v2\/topics\/371942","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":1,"href":"https:\/\/innovationspace.ansys.com\/forum\/wp-json\/wp\/v2\/topics\/371942\/revisions"}],"predecessor-version":[{"id":371943,"href":"https:\/\/innovationspace.ansys.com\/forum\/wp-json\/wp\/v2\/topics\/371942\/revisions\/371943"}],"wp:attachment":[{"href":"https:\/\/innovationspace.ansys.com\/forum\/wp-json\/wp\/v2\/media?parent=371942"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}