Accurate solution for free vibration behaviour of stepped FGM plates implementing the dynamic stiffness method

Abstract

In this article, free vibration response of stepped functionally graded material (FGM) plate is studied through the implementation of dynamic stiffness method (DSM). The material model of the plate is assumed to have the power-law (P-FGM) property variation through the thickness. The kinematic variables within the Kirchhoff’s plate theory are defined by considering the concept of the physical neutral surface to avoid the bending-stretching coupling of the P-FGM plate. The governing equation of motion pertaining to a single plate element are obtained through the application of Hamilton’s principle. Levy type (closed form) solution to this equation of motion is sought to formulate the DS matrix through the implementation of displacement and force edge conditions at the two opposite ends of the plate. The dynamic stiffness (DS) matrix is first formulated for a single FGM plate element and later these DS matrices are suitably assembled to obtain the global DS matrix of the stepped FGM plate. The assembled global DS matrix is finally solved using the Wittrick-William’s algorithm to compute the accurate natural frequencies of the stepped FGM plates. Through different comparisons, it has been demonstrated that the frequency results obtained from the DSM are very accurate for the stepped P-FGM plates. New set of results are also presented by varying different geometrical and material parameter of the stepped plate. The results reported from this parametric study will be beneficial in the design phase of various stepped P-FGM plates.