Three Dimensional Vibration of an Isotropic Plate Enclosed in a Rigid Body

Abstract

In this study, vibration of plates embedded in a rigid enclosure has been investigated analytically for the first time in the literature. It is assumed that the isotropic plate is always in contact with outer enclosure. Therefore, the normal displacement at a boundary surface is constrained but tangential displacement at a surface is allowed. The displacement field is assumed in trigonometric function form. This analytical solution is the only available exact solution of three-dimensional isotropic plate. Numerical results were presented for various geometrical parameters. It is believed that the present formulation and the results can be used as a benchmark for the numerical methods where the exact solution is not possible.

Keywords

• vibration
• three-dimensional isotropic plate
• exact solution
• plate enclosed in a rigid
• trigonometric function form