ABSTRACT
This chapter shows the use of powerful two-dimensional boundary characteristic orthogonal polynomials in the Rayleigh–Ritz method for the free vibration of nonhomogeneous plates. It also shows how the nonhomogeneity, if it occurs on a plate structure owing to the imperfections of the material, can be theoretically investigated for its vibration characteristics. Nonhomogeneous elastic plates are widely used now-a-days in the design of space vehicles, modern missiles, aircraft wings, etc. The nonhomogeneity that occurs in the bodies is especially due to the imperfections of the materials. A design engineer can directly see the presented plots of the figures to have the knowledge about a particular mode for any of the aspect ratio of the nonhomogeneous plate, to finalize the design of the structure. The methodology can be easily extended to various other types of nonhomogeneity in plates with complex geometry.
