Nonlinear oscillations of cracked large-amplitude vibrating plates subjected to harmonic loads

This study investigates the nonlinear dynamics of a cracked plate undergoing large-amplitude vibration, aiming to show the influence of structural damage on the nonlinear characteristics of the plate. First, the governing equations of the cracked large-amplitude vibrating plate are derived by the von Karman theory, with the central part-through crack being simulated by a modified line-spring model for characterizing the crack-induced reduction in stress values. Second, the acquired partial differential equations are discretized by the Galerkin method combined with a simply supported boundary condition. Third, the harmonic balance method and the fourth-order Runge-Kutta algorithm are used to obtain the analytical and numerical approximations of the structural responses, respectively. For cases of small harmonic loads, the plate shows a hardening nonlinear frequency response. Influences of various parameters on this hardening nonlinearity are presented, including crack stage, aspect ratio, plate thickness, excitation location, and excitation amplitude. In cases of large harmonic loads, the bifurcations and chaotic dynamics of the cracked plate are explored by considering the effects of excitation amplitude and excitation frequency. Both analytical and numerical results indicate that a thick plate with a large aspect ratio is more sensitive to damage, especially when the crack parallels to the long side of the plate. Besides, the excitation that occurs far from the plate center with a large amplitude is beneficial for the damage characterization. Particularly, the damage-induced periodic-chaotic transition provides a novel insight into characterizing structural damage from perspectives of chaotic dynamics.

Automated summary

This study investigates the nonlinear dynamics of a cracked plate undergoing large-amplitude vibration and explores the influence of structural damage on the nonlinear characteristics of the plate. Various parameters affecting the nonlinear response, such as crack stage, aspect ratio, and excitation location, are discussed. Results show that the presence of a crack makes the plate more fragile, especially when the crack is parallel to the long side of the plate.