Quintic splines in the study of transverse vibrations of non-uniform orthotropic rectangular plates

An analysis and numerical results are presented for free transverse vibrations of orthotropic rectangular plates of linearly varying thickness along one direction and resting on an elastic foundation of the Winkler type on the basis of classical plate theory. Following the Levy approach i.e., two parallel edges being simply supported, the fourth order differential equation governing the motion of such plates has been solved by using the quintic splines interpolation technique for three different combinations of clamped, simply supported and free boundary conditions at the other two edges; The effect of the elastic foundation together with the orthotropy, aspect ratio and thickness variation on the natural frequencies of vibration is illustrated for the first three modes of vibration. Normalized displacements are presented for two different values of the taper constant keeping other plate parameters fixed for all the three boundary conditions. A comparison of the results: with those available in literature is presented. (C) 1997 Academic Press Limited.