Nonlinear active vibration control of variable-thickness smart sandwich panel under impact loads

In the field of aerospace engineering, the variable-thickness graphene-reinforced porous sandwich (VT-GRPS) panels can be widely applied to critical structures such as spacecraft cabin walls and aircraft wings, serving as a key design strategy for achieving lightweight and performance-optimized configurations. The elastic foundation beneath such structures reflects the actual interaction between the plate and its supporting base. Considering that aircraft are susceptible to intense impact loads during the landing phase, which may induce significant vibrations, research on effective vibration control for such structures is of great importance. The innovation of this paper is to establish the electro-mechanical-elastic coupling dynamic equation of the VT-GRPS plate with Macro Fiber Composite (MFC), and to study the active vibration control (AVC) of the system under impact load. The VT-GRPS panel located on the Winkler-Pasternak elastic foundation (W-PEF) consists of metal aluminum face sheets and the graphene-reinforced porous (GRP) core, with two MFC patches bonded to its surfaces serving as the sensor and actuator, respectively. The paste location of MFC is optimized by genetic algorithm (GA). The boundary conditions of the VT-GRPS panel are simulated using springs with tunable stiffness. According to the Rayleigh-Ritz method, the free vibration are investigated for the VT-GRPS panel. Compared with the mode experiment and ANSYS software, the accuracy is verified for this method. By the lagrange equation, the nonlinear control equations are given for electro-mechanical-elastic coupling in the first two modes. Two transverse impact loads are considered, namely, step loads and decreasing loads, to investigate their respective influences on the AVC of VT-GRPA laminated panels. According to the Runge-Kutta method, the waveforms and external control voltage (ECV) curves are further solved for the VT-GRPS panel and the influence of the change is studied for each parameter on AVC. It is revealed that the MFC paste position optimized by GA has the best control effect. This paper provides a useful idea and method for solving the nonlinear AVC of panel structures with arbitrary boundary conditions.