The flexibility function approach to vibration analysis of rectangular plates with arbitrary multiple point supports on the edges

Abstract

The development and application of a comprehensive analytical technique for the simulation of point supports in the vibration analysis of plates have been presented in some recent studies. The approach was based on simulating a point support on free edges as a zero of a flexibility function, representing a fictitious elastic restraint distribution over the free edge. In these earlier studies mainly a single point support on a free edge was considered. In the present study this technique, namely the flexibility function approach, is extended to a more general class of problems of free vibrations of multiply point supported plates. The versatility and the ability of this approach in simulating arbitrarily located multiple point supports on free edges is demonstrated by considering a rectangular plate with simple supports on two opposite edges and arbitrarily located multiple point supports on the other two edges, which are otherwise free. Numerical results in the form of frequency tables and mode shape plots are presented for wide variety of problems and are compared with those obtained by using the impulse function approach based on epresenting the reactions at the point supports as a Fourier series expansion of the impulse function. This comparative study, while presenting results from these two approaches for the first time, also brings out the superiority of the flexibility function approach.