NONLINEAR VIBRATIONS OF COMPOSITE CANTILEVER PLATE IN SUBSONIC AIR FLOW

With the development of materials science, more and more new materials have been applied to engineering practice. Under the action of airflow excitation, the nonlinear dynamics of plate and shell structures with composite materials based on aerospace engineering is still a hot research topic. In this work, the nonlinear vibrations and responses of a laminated composite cantilever plate under subsonic air flow are investigated. According to the flow condition of ideal incompressible fluid and the Kutta--Joukowski lift theorem, the subsonic aerodynamic lift on the three-dimensional finite length flat wing is calculated by using the Vertex Lattice (VL) method, which is applied to the cantilever plate. The finite length flat wing is modeled as a laminated composite cantilever plate based on the Reddy's third-order shear deformation plate theory, moreover 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 partial differential equations are separated into two nonlinear ordinary differential equations via Galerkin method. Through comparing the natural frequencies of the system with different material and geometry parameters, the 1:2 internal resonance is considered here using multiple scales method. Corresponding to several selected parameters, the frequency-response characteristics are obtained. The hardening-spring-type behaviors and jump phenomena are exhibited.