Free Vibration of Variable Thickness Plates Using Characteristic Orthogonal Polynomial Strip Functions Subjected To Different Combinations of Boundary Conditions

Abstract

A set of characteristic orthogonal polynomial strip functions was used to study the flexural vibration of variable thickness plates in one direction. The starting function in the set, which is satisfying the geometry and natural conditions, is developed from the solution of a static beam subjected to an arbitrary load that expanded into a Taylor series. The Gram-Schmidt orthogonalization process is used to generate the reminder functions of the set. The natural frequencies of the plat are calculated by using the finite strip method together with the transition matrix. Numerical results are obtained for different combination of boundary conditions, tapered ratio and aspect ratio. It is demonstrated that the method as well as the orthogonal strip functions yield good accuracy and fast convergence by comparisons with available results in the literature. This technique can also be used to solve some other complicated problems in the engineering applications.