Abstract
Benchmark vibration solutions for thick polygonal plates of arbitrary boundary conditions are presented. The Mindlin first-order shear deformation theory is used to derive the energy functional while the pb-2 Ritz method is employed for solution. By minimizing the difference between the maximum strain and kinetic energies with respect to unknown coefficients in the pb-2 admissible functions, the governing eigenvalue equation is derived. The vibration frequencies are obtained by solving this governing eigenvalue equation. A convergence study has been carried out to verify the accuracy of these results. In the absence of existing results for thick polygonal plates, the present results where possible are compared with available thin plate solutions by setting the thickness to apothem ratio to be very small (say, t/r=0.001). Sets of first known vibration frequencies for moderately thick regular polygonal plates are presented as an enhancement to existing literature.
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