Effect of crack characteristics on the vibration behavior of post-buckled functionally graded plates

Abstract

This study investigates the free vibration analysis of a cracked post-buckled functionally graded plate under a uniaxial compressive load. The crack is assumed to be open-edged and modeled using a linear, rotational spring. The material is distributed through its thickness gradually. The nonlinear differential equations of motion are derived using the Mindlin plate theory for an initially imperfect plate. First, the nonlinear static differential equations are converted to algebraic equations using the differential quadrature method and solved by an arc-length strategy. The solution of the post-buckling equations gives the equilibrium state of the vibration. Next, the results were implemented into the motion equations to derive the vibrational differential equations. Then, the solution of the standard linearized eigenvalue problem, using the differential quadrature method, results in the plate's natural frequencies and mode shapes. The study compares the effects of various plate parameters on its vibrational behavior before and after buckling. It can be an excellent reference to consider the effect of crack characteristics on vibrations of the functionally graded plates before and after buckling. The presented results agree well with those available in the literature and those computed from the finite element method.