Transverse Vibration of Elliptic and Circular Plates
This chapter addresses the method of solution and the results for the elliptic and circular plates with uniform thickness and discusses the method for elliptic and circular plates. The boundary may be clamped, simply supported, or completely free. The method is based on the use of boundary characteristic orthogonal polynomials (BCOPs) satisfying the essential boundary conditions of the problem. The Rayleigh–Ritz method using BCOPs provides a highly accurate and computationally efficient scheme for finding the vibration characteristics of transverse vibration of elliptic and circular plates. This has already been demonstrated by several authors and the studies carried out by this author have been cited in the references. Various researchers have used different methods to determine the results for clamped elliptic plates. Since the circular plates have been studied in detail, a comparison of their results with the known results serves as a test for the efficiency and powerfulness of the method.