Vibration Analysis of a Thin Elliptical Plate Resting on Winkler Foundation in Hygrothermal Environment Conditions

Abstract

This article presents the non-dimensional natural frequency of a thin elliptical plate lying on an elastic substrate. The Winkler-type elastic foundation has been assumed for the study. The plate under consideration is subjected to hygrothermal environment. The plate’s edges are assumed to be under two separate edge constraints: simply supported and clamped. Classical plate theory in conjugation with Rayleigh–Ritz approach is used to derive and solve the governing equations. To satisfy the different boundary conditions, algebraic polynomials are utilized. In this presented mathematical method, the essential edge constraints have been satisfied rather than considering the natural edge constraint, and based on the obtained admissible functions, the displacement is defined. The described technique has the benefit of being able to handle every combination of edge restrictions effectively, even in the presence of an external environment. In order to validate the suggested model, the non-dimensional natural frequencies computed by the current process are compared with those found in the available literature. The non-dimensional frequencies of elastically supported elliptical plates with varying aspect ratios, edge limitations, and foundation parameters have been reported after convergence and comparison. The reported results show that the non-dimensional frequency increases with an increase in aspect ratio of the plate.