Vibration of non-homogeneous plates using two-dimensional orthogonal polynomials as shape functions in the Rayleigh

Abstract

This paper presents the use of two-dimensional boundary characteristic orthogonal polynomials as the shape functions in the Rayleigh—Ritz method to study the vibration of non-homogeneous plates with a curved boundary, and of elliptical plates in particular. The non-homogeneity considered here is a sort of generalized radial tapering that belongs to a special class such that the taper always extends to zero elasticity and zero density at the plate edges. The first five natural frequencies are reported here for various combinations of the degrees of non-homogeneity. Plots have been presented to show the effect of the aspect ratio on different modes of vibrations for various shapes of elliptic plates and degrees of non-homogeneity. The results for non-homogeneous elliptical plates are entirely new and are not available elsewhere. Comparison can only be made for homogeneous plates, and in this case the results have been found to be in exact agreement with the results of available literature.

Keywords

non-homogeneous orthogonal polynomials elliptical plate Rayleigh-Ritz method vibration

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Vibration of non-homogeneous plates using two-dimensional orthogonal polynomials as shape functions in the Rayleigh—Ritz method

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