Dynamic instability of rectangular plate with an edge crack

In this study, the dynamic instability and non-linear response of the cracked plates subjected to period in-plane load are theoretically analyzed. By applying the Galerkin's method to the dynamic analog of the von Karman's plate equations, the governing equation of a cracked plate is reduced to a time-dependent Mathieu equation. The incremental harmonic balance (IHB) method is applied to solve the non-linear temporal equation of motion and analyze the dynamic instability in this study. Calculations are carried out for the rectangular plates of various aspect ratios under different values of crack ratio conditions. Regions of parametric instability are presented in the spaces of the excitation load versus natural frequency and the natural frequency versus amplitude. In particular, the amplitude of vibration of the plate is considered as an additional parameter of the system. Therefore, the effects of various system parameters on the regions of instability and the non-linear response characteristics of rectangular cracked plates have been investigated and discussed in this study.