A Rayleigh-Ritz approach to transverse vibration os isotropic polygonal plates with variable thickness

OSCAR GROSSI, RICARDO; GRACIELA NALLIN, LIZ; LUCCIONI , BIBIANA MARÍA

Proc. Instn. Mech. Engrs.: Journal of Multi-body Dynamics.

SAGE

Año: 2002 vol. 216 p. 213 - 222

1464-4193

This paper presents a simple, computationally efficient and highly accurate numerical model for the study of free vibration behaviour of polygonal plates with variable thickness. The approach developed is based on the Rayleigh-Ritz method and the use of non-orthogonal right triangular coordinates. The deflection of the plate is approximated by a set of beam characteristic orthogonal polynomials generated using the Gram-Schmidt procedure. The algorithm is quite general and can be used to study plates with any combinations of clamped, simply supported and free edge support conditions and also different taper and geometric parameters. Several examples are solved and some results are compared with existing values in the literature. New results are also presented for tapered polygonal plates with different geometrical shapes and combinations of boundary conditions. For some polygonal plates, their mode shapes of free vibration are shown. The study of this problem is of practical importance for a better understanding of the vibration of polygonal plates which are commonly encountered in modern technology.