Static and dynamic analysis of rectangular plates with linearly varying thickness

In the recent past, there has been a phenomenal increase in the use of plates of uniform/non-uniform thickness due to the desirability of lightweight, high strength, corrosion resistance and high-temperature performance requirements in modern technology. Plates of various materials are widely used in many engineering structures and machines. Their design requires an accurate determination of natural frequencies and mode shapes. As an important numerical computational method, the finite difference method has broad applications in various engineering problems. In this paper, rectangular isotropic plates of linearly varying thickness in one direction are analyzed using finite difference method. Various combinations of boundary conditions are taken and the variation is studied. The static deflections are found out with reasonable accuracy by adopting a suitable mesh size. Dynamic analysis is carried out to find out frequency parameters for the first three modes of vibration. The aspect ratio is varied and the results are compared with those available in literature and are found to be in close agreement. Suggestions regarding the choice of optimum thickness variation are also given.