Nonlinear dynamics analysis of a thin rectangular plate in subsonic airflow

摘要

The bifurcation and chaotic motion of a fully simply-supported thin rectangular plate considering nonlinear deflection subjected to axial subsonic airflow and transverse harmonic excitation is analyzed. Based on von Karman's large deformation theory, the partial differential equation of motion of the structural system is formulated using Hamilton's principle, and it is transformed into a set of ordinary differential equations (ODEs) through Galerkin's method. The three-dimensional (3D) aerodynamic pressure induced by the transverse motion of the plate is derived from the linear potential flow theory, and the validity of the aerodynamic model is verified. For the structural system, Melnikov's method is adopted to give an analytical expression of the necessary condition for the chaotic motion of the plate. The influences of the flow velocity and the external harmonic excitation on the chaotic motion of the plate are investigated. Numerical simulations are carried out to obtain the bifurcation diagrams, displacement time histories, phase portraits, and Poincare maps of the nonlinear system to verify the validity of the analytical results. The results show that when the flow velocity increases, the plate will be unstable, and chaotic motion of the plate will occur.