The free vibrations of tapered rectangular plates using a new set of beam functions with the Rayleigh-Ritz method

Abstract

In this paper, the free vibrations of a wide range of non-uniform rectangular plates in one or two directions are considered. The domain of the plate is bounded by x = α1a, a and y = β1b, b in rectangular co-ordinates. The thickness of the plate is continuously varying and proportional to the power function xsyt. A variety of tapered rectangular plates can be described by giving the taper factors, s and t, different values, s and t may be given arbitrary real numbers if both α1 ≠ 0 and β1 ≠ 0 or arbitrary non-negative numbers if α1 = 0 or β1 = 0. The uniform rectangular plate is a special case by letting both s and t equal to zero. A new set of admissible functions which are the static solutions of the tapered beam (or a strip taken from the tapered rectangular plate), under an arbitrary static load expanded into a Taylor series, is developed. Unlike conventional admissible functions, the set of static beam functions will vary appropriately with the thickness variation of the plate. The eigenfrequency equation is obtained by the use of the Rayleigh-Ritz method. A general computer program has been compiled and some numerical results are tabulated. On the basis of comparison with available results in the literature, it is shown that the first few eigenfrequencies can be obtained with good accuracy by using only a small number of terms of the static beam functions. © 1999 Academic Press.