Vibration and sound radiation analysis of rectangular plates resting on Winkler foundation in thermal environment with closed form solutions

Abstract

This article studies the structural and acoustic responses of a rectangular plate resting on the Winkler foundation under thermal environment. The solutions for the vibration analysis are based on a closed form method, and the Rayleigh integral method is adopted to predict sound radiation from the vibrating heated plate. Not only can the cases with any combination of simply supported and clamped boundary conditions be readily dealt with, but boundary conditions with free edges and the other pair of parallel edges simply supported can also be well considered. Under the current framework, the corresponding frequency equations and mode functions which are simpler than those by the traditional methods are formulated. An excellent accuracy of the proposed method can be observed by comparing the obtained results with the numerical results. Moreover, a considerable number of numerical examples are carried out to reveal the influence of key parameters on the dynamic and acoustic responses of the rectangular plate. Different combinations of the plate geometries, temperature changes, stiffness values of Winkler foundation, and boundary conditions are considered. The proposed method can be employed to investigate the vibration and sound radiation problems of plate subjected to thermo-mechanical loads for all kinds of combinations of simply supported and clamped boundary conditions and a few cases involving free edges.