Study on Free Vibration of Buckled Cracked Plates Using Differential Quadrature Element Method

Vibration of postbuckled cracked plate has been investigated using the differential quadrature element method. The crack modeled as an open crack using a no-mass linear spring. The governing equations of vibration of a buckled cracked plate are derived using the Mindlin theory and considering the effect of initial imperfection. The answer consist of static and dynamic parts. First, differential equations are discretized using the differential quadrature element method and then the resulting nonlinear algebraic equations are solved using the arc-length strategy. Then, 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 to a non-standard eigenvalue problem. Finally, natural frequencies and mode shapes of the buckled cracked plate are obtained solving the eigenvalue problem. The accuracy of the proposed approach is verified using the results obtained by an experimental setup and those obtained by the finite element method. Moreover, several case studies of buckled cracked plates have been solved and effects of selected parameters have been studied.