Bifurcation Studies on a Simply-supported Rectangular Plate with an All-over Part-through Breathing Crack

Abstract

This paper addresses, considering different breathing cracks, the influence of the external excitation frequencies and amplitudes on the nonlinear dynamic responses of plate. The all-over breathing crack on the plate surface having arbitrary depth and location is assumed to be non-propagating and parallel to one side of the plate. A line spring model is used to describe the elastic behavior of the plate at crack location. Considering the equations of motion, simply-supported boundary conditions at four edges and the inner boundary conditions, frequencies and mode shapes are obtained. Using the Galerkin method, we get the ordinary differential equations of breathing crack plate. Finally, through numerical simulations, we obtain the bifurcation diagrams of the cracked plate. Considering different breathing cracks, crack depth ratio and crack relative location, we investigate the effect of external excitation on nonlinear dynamic responses of plate. We find that the breathing crack has much effect on nonlinear dynamic responses of plate, which has important reference value for further research.