Exact closed-form frequency equations for thick circular plates using a third-order shear deformation theory |
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| Authors: | Sh. Hosseini-Hashemi H. Rokni Damavandi Taher M. Fadaie |
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| Affiliation: | a Impact Research Laboratory, School of Mechanical Engineering, Iran University of Science and Technology, Narmak, Tehran 16846-13114, Iran
b School of Engineering, University of British Columbia Okanagan, Kelowna, BC, Canada V1V 1V7 |
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| Abstract: | This paper presents, for the first time, exact closed-form frequency equations and transverse displacement for thick circular plates with free, soft simply supported, hard simply supported and clamped boundary conditions based on Reddy's third-order shear deformation theory. Hamiltonian and minimum potential energy principles are used to extract the equations of dynamic equilibrium and natural boundary conditions of the plate. The new formulation is verified by comparing the results with their counterparts reported in open literature. Natural frequencies of circular plates with different boundary conditions are tabulated in dimensionless form for various values of thickness-radius ratios. The results presented on the basis of exact, closed-form frequency equations are expected to serve as reliable benchmarks. |
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