Accurate Analytical-Type Solutions for the Free Vibration of Simply-Supported Parallelogram Plates

Abstract

A comprehensive study of the free vibration of simply-supported parallelogram plates is conducted. Solutions are obtained by utilizing the superposition method and by taking advantage of symmetry inherent in the problem. Toward this end a new alternating Lévy-type solution is introduced. Verification tests are conducted by comparing computed eigenvalues with those of rhombic plates in the special case where all plate edges are of equal length. Eigenvalues are stored for eight vibration modes and for a wide range of plate geometry.