Stability and vibration properties of a composite laminated plate subjected to subsonic compressible airflow

Abstract

The stability and nonlinear vibration of a composite laminated plate with simply supported boundary conditions in subsonic compressible airflow subjected to transverse periodic external excitation are investigated. The equation of motion of the plate is established by using the von Karman’s nonlinear plate theory. The linear potential flow theory considering the compressibility of the airflow is adopted to formulate the aerodynamic model. The nonlinear ordinary differential equation of motion of the plate is obtained by applying the assumed mode method. The critical divergence velocity and the flutter velocity of the plate are obtained by analyzing the natural frequencies of the linear system. The effects of the ply angle and the compressibility of the airflow on the critical divergence velocities and the flutter velocities of the plate are investigated. For the nonlinear system, the displacement time response of the plate subjected to accelerating airflow and transverse harmonic excitation is presented to investigate the vibration properties. The effects of the subsonic airflow on the resonance properties of the system are analyzed from the amplitude frequency curves of the plate under different flow velocities. From the study, it can be seen that with the flow velocity increasing, the natural frequencies of the plate decreases and the plate may exhibit instability of the divergence or flutter type. With the ply angle increasing from 0° to 90°, the critical divergence velocity increases and then decreases, and the flutter velocity decreases. The critical divergence velocity and the flutter velocity of the plate obtained from the compressible aerodynamic model are smaller than those obtained from the incompressible model. When the plate is in instability of divergence type, the plate vibrates with smaller amplitude around a non-zero point of equilibrium, and when the plate is in instability of flutter type, the plate vibrates with larger amplitude around a non-zero point of equilibrium. When the flow velocity exceeds the divergence velocity, the amplitude frequency curve of the plate is an irregular curve with larger vibration amplitudes and the plate may be in a chaotic motion state.