Exact solution for frequency equations of radial and transverse vibration of a circular plate with various boundary conditions

Document Type : Research Paper

Authors

Abstract

In this study, closed-form relations are obtained for the frequency equations of radial (in-plane) and transverse (out-of–plane) free vibration of a circular plate with free, simply-support, and clamped boundary conditions. Governing equations are obtained using Hamilton's principal. In the case of radial vibration, governing equations are coupled to each other. So, they are decoupled using Helmholtz decomposition technique and solved using separation of variables method. In the case of transverse vibration, governing equations are analytically solved using separation of variables method. Finally, natural frequencies obtained from the frequency equations are compared with finite element results for an isotropic homogeneous circular plate with various boundary conditions.

Keywords


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