Table 5 Example 5, Dimensionless frequency parameter O2 ( Q = 1/3, k = 2, r = 0.4) Present approach Mode Ref. [15] 4u11 dofs 7u11 dofs 4u22 dofs 1 36.347 36.398 36.382 36.298 2 41.041 41.516 41.283 41.428 3 54.029 55.828 55.114 55.349 4 62.686 65.382 64.625 63.759 5 77.093 77.605 77.287 76.327 6 82.638 86.545 86.362 82.690 1 0.5 0 -0.5 -1 0.5 0 -0.5 0 Mode 1 -1 -0.5 0 0.5 1 0.5 0 -0.5 0 0.5 Mode 2 -1 -0.5 0 0.5 1 0.5 0 -0.5 0 0.5 Mode 3 1 0.5 0 -0.5 -1 -0.5 0 0.5 0 0.5 Mode 4 -1 -0.5 0 0.5 1 0.5 0 -0.5 0 0.5 Mode 5 -1 -0.5 0 0.5 1 0.5 0 -0.5 0 0.5 Mode 6 Fig. 10 Clamped-free elliptic annular plate ( Q = 1/3, k = 2, a = 1, r = 0.4): modes 1 to 6 87
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