Differential transform method to study free transverse vibration of monoclinic rectangular plates resting on Winkler foundation

Abstract

This paper analyses free transverse vibration of a monoclinic rectangular plate of uniform thickness resting onWinkler foundation using differential transform method (DTM). Two parallel edges of the plate are taken according to Levy approach i.e., simply supported and other two edges may be either clamped-clamped or clamped-simply supported. This semi-numerical-analytical technique converts the governing differential equation and boundary conditions into a set of algebraic equations. Characteristic equations have been obtained for above two combinations of boundary conditions in the form of infinite series and solved numerically by truncating these equations to finite number of terms. Robustness and convergence of the method is confirmed through numerical results. Two dimensional and three dimensional mode shapes have been plotted for both the cases.