EFFECTS OF BOUNDARY CONSTRAINTS AND THICKNESS VARIATIONS ON THE VIBRATORY RESPONSE OF RECTANGULAR-PLATES

The present study concentrates on the first known free flexural vibration of doubly-tapered rectangular plates subject to a variety of boundary constraints ranging from a cantilevered plate to a fully clamped plate. The Rayleigh-Ritz minimum total energy approach complemented by the global pb-2 shape functions as the admissible plate displacement amplitude functions is employed. The shape functions are, in principle, the product of a set of mathematically complete two-dimensional polynomials and a basic function. The basic function is formed from a product of the boundary piecewise geometric expressions of the plate each of which is raised to the power of 0, 1 or 2 corresponding to a free, simply supported or clamped edge, respectively. The shape functions satisfy the kinematic boundary conditions at the outset. This proposed computational model has a great advantage over the conventional finite element and the finite strip methods in terms of computation cost, numerical preparation and implementation, application versatility, and, in certain aspects, numerical accuracy. Comprehensive numerical results for six classes of plates with selected mode shapes are presented. These results may serve as a benchmark for future reference since no literature can be found for symmetric doubly-tapered plates as considered in this study.