A Power Series Solution for Free Vibration of Variable Thickness Mindlin Circular Plates with Two-Directional Material Heterogeneity and Elastic Foundations

Abstract

In the present paper, a semi-analytical solution is presented for free vibration analysis of circular plates with complex combinations of the geometric parameters, edge-conditions, material heterogeneity, and elastic foundation coefficients. The presented solution covers many engineering applications. The plate is assumed to have a variable thickness and made of a heterogeneous material whose properties vary in both radial and transverse directions. While the edge is simply-supported, clamped, or free; the bottom surface of the plate is resting on a two-parameter (<em>Winkler-Pasternak</em>) elastic foundation. A comprehensive sensitivity analysis including evaluating effects of various parameters is carries out. <em>Mindlin</em> theory is employed for derivation of the governing equations whereas the differential transform method is used to solve the resulted equations. In this regard, both the in-plane and rotary inertia are considered. Results show that degradations caused by a group of the factors (e.g., the geometric parameters) in the global behavior of the structure may be compensated by another group of factors of different nature (e.g, the material heterogeneity parameters). Moreover, employing the elastic foundation leads to higher natural frequencies and postponing the resonances.