{"id":10875,"date":"2023-11-15T10:24:30","date_gmt":"2023-11-15T10:24:30","guid":{"rendered":"https:\/\/support.buildsoft.eu\/?post_type=ht_kb&p=10875"},"modified":"2024-04-15T07:26:05","modified_gmt":"2024-04-15T07:26:05","slug":"thin-circle-fixed-at-two-points-eigen-frequencies","status":"publish","type":"ht_kb","link":"https:\/\/support.buildsoft.eu\/es\/knowledge-base\/thin-circle-fixed-at-two-points-eigen-frequencies\/","title":{"rendered":"DLX 04: Thin circle – fixed at two points – eigen frequencies"},"content":{"rendered":"

Description<\/h2>\n

\"\"
\n

\n\n\n\n\n\n\n\n\n\n
Material<\/th>\n<\/td>\nModulus of elasticity<\/td>\n\"E=7 200 000 N/mm^2\"<\/td>\n<\/tr>\n
<\/td>\nDensity<\/td>\n\"\rho=2700 kg/m^3\"<\/td>\n<\/tr>\n
Geometry<\/th>\nCross-section<\/td>\n<\/td>\n\"b = 10 mm\"<\/td>\n<\/tr>\n
<\/td>\n<\/td>\n\"h = 5 mm\"<\/td>\n<\/tr>\n
Boundary conditions<\/td>\nIn points A at angle \"\alpha=120 ^{\circ}\"<\/td>\nFixed support<\/td>\n<\/tr>\n
<\/td>\nAlong the entire edge<\/td>\n\"R_z, M_x\" and \"M_y\" fixed to impose 2D behaviour<\/td>\n<\/tr>\n
Mesh<\/th>\n<\/td>\nNo. of divisions<\/td>\n8<\/td>\n<\/tr>\n<\/tbody>\n<\/table>\n<\/div>\n

Results<\/h2>\n
<\/span>Handcalculation<\/div>
\n

  <\/span>   <\/span>\"\[f_i=\frac{1}{2\cdot \pi}\cdot \lambda_i\cdot \frac{h}{R^2}\cdot \sqrt{\frac{E}{12\cdot \rho }}\]\"<\/p>\n

  <\/span>   <\/span>\"\[<\/p>\n<\/div><\/div><\/div>\n

\n\n\n\n\n\n\n\n\n\n\n
Eigen mode<\/th>\nShape<\/th>\nIndependent reference<\/th>\nDiamonds<\/th>\nDifference<\/th>\n<\/tr>\n
1<\/td>\n\"\"<\/td>\n23.5Hz<\/td>\n23.6Hz<\/td>\n-0.31%<\/td>\n<\/tr>\n
2<\/td>\n\"\"<\/td>\n57.5Hz<\/td>\n57.8Hz<\/td>\n-0.47%<\/td>\n<\/tr>\n
3<\/td>\n\"\"<\/td>\n110.6Hz<\/td>\n111.1Hz<\/td>\n-0.48%<\/td>\n<\/tr>\n
4<\/td>\n\"\"<\/td>\n140.6Hz<\/td>\n141.2Hz<\/td>\n-0.45%<\/td>\n<\/tr>\n
5<\/td>\n\"\"<\/td>\n175.1Hz<\/td>\n175.9Hz<\/td>\n-0.45%<\/td>\n<\/tr>\n
6<\/td>\n\"\"<\/td>\n255.7Hz<\/td>\n256.8Hz<\/td>\n-0.43%<\/td>\n<\/tr>\n
7<\/td>\n\"\"<\/td>\n280.1Hz<\/td>\n281.6Hz<\/td>\n-0.52%<\/td>\n<\/tr>\n<\/tbody>\n<\/table>\n<\/div>\n

References<\/h2>\n
\n
    \n
  • M\u00e9caniciens, S. F. D. (1990). Guide de validation des progiciels de calcul des structures: SDLL 12: anneau circulaire mince encastr\u00e9 en deux points
    \n<\/i>The dimensions of the Afnor example were too small for Diamonds. So the radius R and young’s modulus E have been adjusted, and the results are recalculated accordingly.<\/li>\n<\/ul>\n
      \n
    • Tested in Diamonds 2026.<\/li>\n<\/ul>\n\n<\/div>\n","protected":false},"excerpt":{"rendered":"

      Description Results References M\u00e9caniciens, S. F. D. (1990). Guide de validation des progiciels de calcul des structures: SDLL 12: anneau circulaire mince encastr\u00e9 en deux points The dimensions of the Afnor example were too small for Diamonds. So the radius R and young’s modulus E have been adjusted, and the…<\/p>\n","protected":false},"author":3,"comment_status":"closed","ping_status":"closed","template":"","format":"standard","meta":[],"ht-kb-category":[1206],"ht-kb-tag":[],"_links":{"self":[{"href":"https:\/\/support.buildsoft.eu\/es\/wp-json\/wp\/v2\/ht-kb\/10875"}],"collection":[{"href":"https:\/\/support.buildsoft.eu\/es\/wp-json\/wp\/v2\/ht-kb"}],"about":[{"href":"https:\/\/support.buildsoft.eu\/es\/wp-json\/wp\/v2\/types\/ht_kb"}],"author":[{"embeddable":true,"href":"https:\/\/support.buildsoft.eu\/es\/wp-json\/wp\/v2\/users\/3"}],"replies":[{"embeddable":true,"href":"https:\/\/support.buildsoft.eu\/es\/wp-json\/wp\/v2\/comments?post=10875"}],"version-history":[{"count":3,"href":"https:\/\/support.buildsoft.eu\/es\/wp-json\/wp\/v2\/ht-kb\/10875\/revisions"}],"predecessor-version":[{"id":12796,"href":"https:\/\/support.buildsoft.eu\/es\/wp-json\/wp\/v2\/ht-kb\/10875\/revisions\/12796"}],"wp:attachment":[{"href":"https:\/\/support.buildsoft.eu\/es\/wp-json\/wp\/v2\/media?parent=10875"}],"wp:term":[{"taxonomy":"ht_kb_category","embeddable":true,"href":"https:\/\/support.buildsoft.eu\/es\/wp-json\/wp\/v2\/ht-kb-category?post=10875"},{"taxonomy":"ht_kb_tag","embeddable":true,"href":"https:\/\/support.buildsoft.eu\/es\/wp-json\/wp\/v2\/ht-kb-tag?post=10875"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}