Nonlinear Vibrations of Laminated Cross-Ply Composite Cantilever Plate in Subsonic Air Flow

Abstract

The nonlinear vibrations and responses of a laminated composite cantilever plate under the subsonic air flow are investigated in this paper. The subsonic air flow around the three-dimensional cantilever rectangle laminated composite plate is considered to be decreasing from the wing root to the wing tip. According to the ideal incompressible fluid flow condition and the Kutta–Joukowski lift theorem, the subsonic aerodynamic lift on the three-dimensional finite length flat wing is calculated by using the Vortex Lattice (VL) method. The finite length flat wing is modeled as a laminated composite cantilever plate based on Reddy’s third-order shear deformation plate theory and the von Karman geometry nonlinearity is introduced. The nonlinear partial differential governing equations of motion for the laminated composite cantilever plate subjected to the subsonic aerodynamic force are established via Hamilton’s principle. The Galerkin method is used to separate the partial differential equations into two nonlinear ordinary differential equations, and the four-dimensional nonlinear averaged equations are obtained by the multiple scale method. Through comparing the natural frequencies of the linear system with different material and geometric parameters, the relationship of 1 : 2 internal resonance is considered. Corresponding to several selected parameters, the frequency-response curves are obtained. The hardening-spring-type behaviors and jump phenomena are exhibited. The influence of the force excitation on the bifurcations and chaotic behaviors of the laminated composite cantilever plate is investigated numerically. It is found that the system is sensitive to the exciting force according to the complicate nonlinear behaviors exhibited in this paper.