A finite element dynamic model of the sandwich composite plate was developed based on classical laminate theory and Hamilton's principle. A 4-node, 7-degree-of-freedom three-layer plate cell is constructed to simulate the interaction between the substrate, the viscoelastic damping layer, and the piezoelectric material layer. Among them, the viscoelastic layer is referred to as the complex constant shear modulus model, and the equivalent Rayleigh damping is introduced to represent the damping of the substrate. The established dynamics model has too many degrees of freedom, and the obtained dynamics model has good controllability and observability after adopting the joint reduced-order method of dynamic condensation in physical space and equilibrium in state space. The optimal quadratic (LQR) controller is designed for the active control of the sandwich panel, and the parameters of the controller parameters, the thickness of the viscoelastic layer, and the optimal covering position of the sandwich panel are optimized through simulation analysis. The results show that the finite element model established in this paper is still valid under different boundary conditions and different covering methods, and the model can still accurately and reliably represent the dynamic characteristics of the original system after using the joint step-down method. Under different excitation signals and different boundary conditions, the LQR control can effectively suppress the vibration of the sandwich plate. The optimal cover position of the sandwich plate is near the solid support end and far from the free-degree end. The parameters of controller parameters and viscoelastic layer thickness are optimized from several angles, respectively, and a reasonable optimization scheme can be selected according to the actual requirements.
Keywords: LQR controller; finite element modeling; model order reduction; parameter optimization; sandwich composites.