基于高阶剪切变形理论的四边形求积元板单元及其应用1)

申志强, 夏军, 宋殿义, 程盼

A QUADRILATERAL QUADRATURE PLATE ELEMENT BASED ON REDDY'S HIGHER-ORDER SHEAR DEFORMATION THEORY AND ITS APPLICATION1)

Shen Zhiqiang, Xia Jun, Song Dianyi, Cheng Pan

表9 变厚度方板无量纲自振频率$\omega {a^2}/{\pi ^2}\sqrt {{12\rho \left({1 - \nu ^2} \right)}/{Eh_0^2 }} $

Table 9 The dimensionless frequencies of the square plate with variable thickness (Type II, III, IV)

Mode 1 2 3 4 5 6 Type II QEM 13x13 2.7450 5.3082 5.421 8 7.6561 9.0295 9.1302 Ref.[35] 2.7454 5.3031 5.4186 7.6483 9.0192 9.1099 Ref.[36] 2.7392 5.2879 5.4007 7.6143 8.9747 9.0768 Type III QEM 13x13 2.2846 4.3393 4.5317 6.4331 7.3198 7.7467 Ref.[35] 2.2850 4.3375 4.5294 6.4291 7.311 8 7.7358 Ref.[36] 2.281 8 4.3298 4.5207 6.4107 7.2945 7.7157 Type IV QEM 13x13 2.4382 4.2238 4.800 9 6.5089 6.9839 8.0295 Ref.[35] 2.4384 4.2222 4.7987 6.5044 6.9782 8.021 2 Ref.[36] 2.4356 4.2163 4.789 4 6.4882 6.9645 7.9971