Three-dimensional vibration analysis of right triangular thick plates using Chebyshev polynomial and Ritz method

摘要

A three-dimensional (3-D) method of analysis is presented for determining the eigenfrequencies and mode shapes of right triangular thick plates. The actual triangular plate domain is firstly mapped onto a basic cubic domain by the co-ordinate transformation. Then potential (strain) and kinetic energy of the plate are formulated, and the Ritz method is applied to derive the governing eigenvalue equation, based on extremum energy principle. A set of Chebyshev polynomial series multiplied by a boundary function chosen to satisfy the essential geometry boundary conditions of the plate are developed as the admissible functions of every displacement components in each direction. The convergence and comparison studies show that rather accurate results can be obtained by using this approach. The effects of thickness-to-length ratio and length-to-width ratio on eigenfrequencies of the cantilevered and completely free right triangular plates are studied in detail. Sets of valuable results are presented, which may serve as the benchmark reference to future research into the refined plate theories and also for checking the accuracy of new numerical techniques.