Natural Frequencies of Axisymmetric Vibrations of Thin Hyperbolic Circular Plates with Clamped Edges

Abstract

A free vibration analysis of homogeneous and isotropic circular thin plates with nonlinear thickness variation and clamped edges is considered. The limited independent solutions of differential Euler equation were expanded in the power series based on the properties of integral equations. The analytical frequency equations as power series were obtained using the method of successive approximations.

Modelling of Equivalent Mass and Rigidity of Continual Segment of the Inter-Resonance Vibration Machine

“…Srinivasa et al [7] experimentally studied the free vibration frequencies of isotropic and laminated composite plates. Jaroszewicz [8] analyzed the vibration of homogeneous and isotropic circular thin plates with nonlinear variable thickness, which are clamped at the edges. Zur [9] considered the natural vibration of homogeneous and isotropic circular thin plates with variable distributed parameters using Green's functions, which depend on the Poisson coefficient and the coefficient of distribution of the rigidity of the plate on the bend.…”