Free vibration analysis of cracked postbuckled plate

Abstract

• The problem of vibration analysis of cracked postbuckled plates is investigated for the first time. • Crack is modeled as a rotational spring and the effects of initial imperfections and shear deformations are considered. • Static and dynamic nonlinear differential equations are solved. • The results are verified using experimental and finite element data. • The results show that the applied load, geometric imperfection and crack parameters have impact on natural frequencies. In this paper, a methodology is introduced to address the free vibration analysis of cracked plate subjected to a uniaxial inplane compressive load for the first time. The crack, assumed to be open and at the edge is modeled by a massless linear rotational spring. The governing differential equations are derived using the Mindlin theory, taking into account the effect of initial imperfection. The response is assumed to be consisting of static and dynamic parts. For the static part, differential equations are discretized using the differential quadrature element method and resulting nonlinear algebraic equations are solved by an arc-length strategy. Assuming small amplitude vibrations of the plate about its buckled state and exploiting the static solution in the linearized vibration equations, the dynamic equations are converted into a non-standard eigenvalue problem. Finally, natural frequencies and modal shapes of the cracked buckled plate are obtained by solving this eigenvalue problem. To ensure the validity of the suggested approach an experimental setup and a numerical finite element model have been made to analyze the vibration of a cracked square plate with simply supported boundary conditions. Also, several case-studies of cracked buckled plate problem have been solved utilizing the proposed method, and effects of selected parameters have been studied. The results show that the applied load and geometric imperfection as well as the position, size and depth of the crack have different impact on natural frequencies of the plate.