Transverse vibrations of non-homogeneous orthotropic rectangular plates of variable thickness: A spline technique

An analysis and numerical results are presented for free transverse vibrations of non-homogeneous orthotropic rectangular plates of non-uniform thickness and resting on an elastic foundation of Winkler type on the basis of classical plate theory. The non-homogeneity of the plate material is assumed to arise due to the exponential variation in Youngʹs moduli and density along one direction. Following Lévy approach i.e. the two parallel edges are simply supported, the fourth-order differential equation governing the motion of such plates of exponentially varying thickness in one direction, 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. Effect of the non-homogeneity and elastic foundation together with other plate parameters such as 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 specified plates for all the three boundary conditions.