Nonlinear vibration of a two-dimensional composite laminated plate in subsonic air flow

Abstract

The nonlinear vibration of a two-dimensional composite laminated plate in subsonic air flow with simply supported boundary conditions is investigated. Based on the von Karman’s plate theory, the equation of motion of the plate is established using Hamilton’s principle. The aerodynamic pressure induced by the coupled vibration of the plate and subsonic airflow is derived from the linear potential flow theory and compared with the existing model. The variable separation method is used to transform the equation of motion of the plate into nonlinear ordinary differential equations. The influences of the flow velocity, the length-to-thickness ratio and the ply angle of the plate on the nonlinear vibration behaviors of the plate are discussed. From the analytical and numerical results it can be seen that the critical instability velocity obtained from the present aerodynamic model is the same as the existing result. The first-order expansion of the transverse displacement can reflect the dynamic characteristics of the plate. With the increase of the flow velocity and the length-to-thickness ratio, the instability interval of the nonlinear vibration can be prolonged and the nonlinear resonance frequency can be increased. The composite laminated plate with smaller ply angle exhibits more stable dynamic properties than that with larger ply angles.