chapter  12
35 Pages

Plates with Variable Thickness

WithS. Chakraverty

The study of transverse vibration of plates of variable thickness is very important in a wide variety of applications in the industry and engineering. The example of elliptic plate with variable thickness is taken into consideration to understand how the variable thickness plates are to be handled using the method of boundary characteristic orthogonal polynomials (BCOPs). Before going into the details of the methodology and the corresponding results, this chapter discusses some of the works specific to the elliptic plates with variable thickness and utilizes the BCOPs in plates with variable thickness. The chapter introduces the method to handle any variable-thickness property of the plates. The number of approximations is successively increased and the results are compared with the previous approximation. The process is truncated when the desired numbers of frequencies converged to the first three frequencies of each group, viz., symmetric–symmetric, symmetric–antisymmetric, antisymmetric–symmetric, and antisymmetric–antisymmetric modes, to four or five significant digits.