NATURAL FREQUENCIES FOR FREE-VIBRATION OF NONHOMOGENEOUS ELLIPTIC ANDCIRCULAR PLATES USING 2-DIMENSIONAL ORTHOGONAL POLYNOMIALS

The present paper deals with the transverse vibration of nonhomogeneou s elliptic and circular plates using two-dimensional boundary characte ristic orthogonal polynomials in the Rayleigh-Ritz method. The boundar y of the plate may be clamped, simply supported, or free. The nonhomog eneity of the plate is characterized by faking linear variation of the Young's modulus and parabolic variation of the density of the materia l. The first five natural frequencies are reported here for various co mbinations of the parameters of the nonhomogeneity and for different v alues of the aspect ratios of the ellipse. All the results presented h ere are entirety new and are not found elsewhere. Comparison can only be made for homogeneous plates, and in that case the results have been compared with those found in the existing literatures and are in exce llent agreement. (C) 1997 by Elsevier Science.