Rectangular and Skew Plates
This chapter focuses on the use of the method of boundary characteristic orthogonal polynomials (BCOPs) in the study of the vibration of skew plates. Free vibration of rectangular, skew, and square plates has been studied extensively throughout the globe using different methods of solutions. In fact, Leissa included most of the results of rectangular and skew plates till that date. Moreover, Gorman published a book, which in particular, is entirely devoted to the vibrations of rectangular plates. The rectangular and skew plates were studied using either one- or two-dimensional orthogonal polynomials, directly by generating the polynomials over their particular domains. However, in this case the rectangular or skew domains are first mapped into a standard unit-square domain. The generated BCOPs have been used in the Rayleigh–Ritz method for determining the vibration frequencies. There are a number of parameters controlling the domain as well as the boundary conditions of the plate.