Three-dimensional Vibration Analysis of Thick Plates on Winkler Foundation

摘要

Many engineering problems can be modeled as isotropic rectangular plates on elastic foundation such as footing of building, pavement of roads and base of heavy machines. The Winkler mode! is widely used to describe the mechanical behavior of the foundation when attention is focused on plate analysis. Many papers about plate vibration on Winkler foundation using the Kirchhoff theory for thin plates and the Mindlin theory for moderately thick plates can be found. However, no research work about the three-dimensional (3D) vibration analysis of thick plates on elastic foundation can be found except that Matsunaga [1] developed a special higher-order plate theory by considering the stress conditions on the upper and lower surfaces of the plate. In this paper, the 3D vibration characteristics of rectangular thick plates with arbitrary boundary conditions and resting on Winkler foundation have been studied by using the Ritz method. The analysis procedure is based on the exact linear, small-strain elasticity theory. The Chebyshev polynomials [2], multiplied by a boundary function to satisfy the geometric boundary conditions, are taken as the basic functions [3]. Convergence and comparison studies demonstrate the high accuracy of the present method. The thickness and the foundation stiffness on vibration characteristics of rectangular plates are studied in detail.