{"id":10898,"date":"2023-11-16T08:17:12","date_gmt":"2023-11-16T08:17:12","guid":{"rendered":"https:\/\/support.buildsoft.eu\/?post_type=ht_kb&p=10898"},"modified":"2024-12-17T14:58:13","modified_gmt":"2024-12-17T14:58:13","slug":"dls-04","status":"publish","type":"ht_kb","link":"https:\/\/support.buildsoft.eu\/es\/knowledge-base\/dls-04\/","title":{"rendered":"DLS 04: Circular plate fixed at inner edge – eigenfrequencies"},"content":{"rendered":"

Description<\/h2>\n

\"\"<\/p>\n

\n\n\n\n\n\n\n\n\n\n
Material<\/th>\n<\/td>\nModulus of elasticity<\/td>\n\"E=200 000 N/mm^2\"<\/td>\n<\/tr>\n
<\/td>\nDensity<\/td>\n\"\rho=7800 kg/m^3\"<\/td>\n<\/tr>\n
<\/td>\nPoisson\u2019s ratio<\/td>\n\"\nu= 0.3\"<\/td>\n<\/tr>\n
Geometry<\/th>\nCross-section<\/td>\nThickness<\/td>\n\"e = 10mm\"<\/td>\n<\/tr>\n
Boundary conditions<\/td>\nAlong the inner circle<\/td>\nFixed support<\/td>\n<\/tr>\n
Mesh<\/th>\n<\/td>\nMaximum element size<\/td>\n\"0.20m\"<\/td>\n<\/tr>\n
<\/td>\nMinimum element size<\/td>\n\"0.00m\"<\/td>\n<\/tr>\n<\/tbody>\n<\/table>\n<\/div>\n

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

  <\/span>   <\/span>\"\[f_i=\frac{1}{2\cdot \pi \cdot R^2}\cdot \lambda_{ij} \cdot \sqrt{\frac{E \cdot e^2}{12\cdot (1-\nu^2) }}\]\"<\/p>\n

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

\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>\n7.93Hz<\/td>\n8.00Hz (M1)<\/td>\n0.93%<\/td>\n<\/tr>\n
2<\/td>\n\"\"<\/td>\n8.11Hz<\/td>\n8.15Hz (M2)<\/td>\n0.51%<\/td>\n<\/tr>\n
3<\/td>\n\"\"<\/td>\n8.96Hz<\/td>\n9.01Hz (M4)<\/td>\n0.53%<\/td>\n<\/tr>\n
4<\/td>\n\"\"<\/td>\n11.28Hz<\/td>\n11.38Hz (M6)<\/td>\n0.89%<\/td>\n<\/tr>\n
5<\/td>\n\"\"<\/td>\n51.89Hz<\/td>\n53.29Hz (M19)<\/td>\n2.71%<\/td>\n<\/tr>\n
6<\/td>\n\"\"<\/td>\n52.86Hz<\/td>\n53.42Hz (M20)<\/td>\n1.06%<\/td>\n<\/tr>\n
7<\/td>\n\"\"<\/td>\n55.91Hz<\/td>\n54.23Hz (M22)<\/td>\n-3.00%<\/td>\n<\/tr>\n
8<\/td>\n\"\"<\/td>\n60.97Hz<\/td>\n57.57Hz (M24)<\/td>\n-5.58%<\/td>\n<\/tr>\n<\/tbody>\n<\/table>\n<\/div>\n

The difference between the first 4 and last 4 eigen frequencies are the type of shape mode. There are a few shape modes (accompanied by an eigen frequency) between 11.28 en 51.89Hz which are not listed in the table above.<\/p>\n

References<\/h2>\n
\n
    \n
  • M\u00e9caniciens, S. F. D. (1990). Guide de validation des progiciels de calcul des structures: SDLS 04: plaque mince annulaire encastr\u00e9e sur un moyeu
    \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.
    \n<\/i><\/li>\n<\/ul>\n
      \n
    • Tested in Diamonds 2026.<\/li>\n<\/ul>\n\n<\/div>\n","protected":false},"excerpt":{"rendered":"

      Description Results The difference between the first 4 and last 4 eigen frequencies are the type of shape mode. There are a few shape modes (accompanied by an eigen frequency) between 11.28 en 51.89Hz which are not listed in the table above. References M\u00e9caniciens, S. F. D. (1990). Guide de…<\/p>\n","protected":false},"author":3,"comment_status":"closed","ping_status":"closed","template":"","format":"standard","meta":[],"ht-kb-category":[1207],"ht-kb-tag":[],"_links":{"self":[{"href":"https:\/\/support.buildsoft.eu\/es\/wp-json\/wp\/v2\/ht-kb\/10898"}],"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=10898"}],"version-history":[{"count":3,"href":"https:\/\/support.buildsoft.eu\/es\/wp-json\/wp\/v2\/ht-kb\/10898\/revisions"}],"predecessor-version":[{"id":12815,"href":"https:\/\/support.buildsoft.eu\/es\/wp-json\/wp\/v2\/ht-kb\/10898\/revisions\/12815"}],"wp:attachment":[{"href":"https:\/\/support.buildsoft.eu\/es\/wp-json\/wp\/v2\/media?parent=10898"}],"wp:term":[{"taxonomy":"ht_kb_category","embeddable":true,"href":"https:\/\/support.buildsoft.eu\/es\/wp-json\/wp\/v2\/ht-kb-category?post=10898"},{"taxonomy":"ht_kb_tag","embeddable":true,"href":"https:\/\/support.buildsoft.eu\/es\/wp-json\/wp\/v2\/ht-kb-tag?post=10898"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}