Three-dimensional vibration analysis of cantilevered and completely free isosceles triangular plates

Abstract

The free vibration of cantileveredand completely free isosceles triangular plates based on exact three-dimensional elasticity theory is investigated. The actual plate domain is first mapped onto a basic cubic domain. The the Ritz method is applied to derived the eigenfrequency equation from the strain energy and the kinetic energy of the plate. A set of Chebyshev polynomial series multiplied by a boundary function chosen to satisfy the essential geometry boundary conditions of the plate is developed as the admissible functions of each displacement component. The convergence and comparison studies show that rather accurate results can be obtained by using this approach. The effects of thickness-to-width ratio and apex angle on eigenfrequencies of the plates are studied in detail. Sets of valuable results are presented, which may serve as the benchmark values for future numerical techniques in thick plate vibration analysis. Data for the completely free isosceles triangular plates are presented for the first time. © 2002 Elsevier Science Ltd. All rights reserved.