Nonlinear aeroelastic analysis and flutter control of bistable composite laminated cantilever plates

The nonlinear aeroelastic behaviors of bistable composite laminated cantilever plates with pre-strain are presented. An aeroelastic analytical model is developed based on the first-order shear theory (FSDT) for characterizing the structural displacement and linear piston theory for calculating aerodynamic load. The von Karman large deformation theory is adopted to consider the nonlinear effects of pre-strains and temperatures. The differential equation of motion for bistable laminates is derived using the Hamiltonian principle, and the finite element method is utilized to discretize the model. Bifurcation types are analyzed through the nonlinear eigenvalues obtained via the complex mode method and the Newton iterative method. The OSS11 implicit time-domain integrator is used to compute nonlinear time-domain responses. After verifying the correctness of the program and formula with commercial software and existing literature, the impacts of pre-strains, temperatures, geometry, and flow yaw angle are studied, which can significantly affect the aeroelastic stability of bistable composite laminates by various mechanisms. To suppress chaotic behavior, the influences of damping are also considered. Finally, the linear quadratic regulator (LQR) is applied to the control of this strongly nonlinear system. By solving the control laws for different dynamic pressure conditions, effective suppression of the complex dynamic response is achieved.