Numerical computing of frequencies for rectangular and square plates with transcendental thickness variation

Abstract

The frequencies of the thin plate play an important role for the design of the engineering machines, naval structure, etc. Tremendous amount of the literature on the study of vibrations of rectangular and square plate are available with various kinds of the thickness variations. From the study it is observed that transcendental thickness variation has not been studied by the researchers which satisfy the boundary conditions. Therefore, the present work is the attempt in this direction. A well-known Rayleigh-Ritz method has been used for computation of the first three frequencies alongwith mode shapes and by varying the boundary conditions at the side of the plate. The convergence of the computed results has been presented through table and comparison has also been made with the existing result.