Experimental verification and theoretical study on nonlinear vibrations of aluminum-based sandwich airfoil plate under external excitations

In the application domains of tactical reconnaissance and high-speed penetration, unmanned aerial vehicles equipped with low-aspect-ratio wings have garnered significant attention due to their high maneuverability, compact structure, and superior high-speed performance. In this paper, the low aspect ratio wing is taken as the research object, and a dynamic model is established for the unified solution of the airfoil quadrilateral wing. This investigation aims to develop a unified methodology for studying nonlinear vibrations of the graphene-reinforced porous aluminum-based (GRPA) sandwich airfoil quadrilateral (GRPA-SAQ) plates under complex boundary conditions, addressing the critical need for analyzing the aeronautical structures with the irregular geometries and reinforced material properties. The GRPA-SAQ plate model is constructed, combining the GRPA core layer with aluminum face sheets, with the arbitrary boundaries simulated by distributed artificial springs. By introducing the four-node coordinate transformation, the airfoil quadrilateral in the Cartesian coordinate system is transformed into the square domain in the natural coordinate system. Based on the first-order shear deformation theory (FSDT), the strain energy, kinetic energy and boundary spring potential energy of the airfoil quadrilateral plate structure in the natural coordinate system are derived. Based on Chebyshev polynomial, the displacement admissible function of equal square plate is constructed. The nonlinear ordinary differential equations for a system are derived using the Lagrange's equation. The model is validated by comparing the natural vibration obtained from modal testing with those from ANSYS simulations. Furthermore, the qualitative agreement between the amplitude-frequency response curves from frequency sweep experiments and the theoretical results further verified the accuracy of the proposed modeling approach. The experimental results demonstrates that the system shows a trend of hard spring characteristics. Subsequently, considering the 1:3 internal resonance of GRPA-SAQ plate, a multi-scale method is adopted in perturbation analysis to obtain the average equation in polar coordinate system for nonlinear response theoretical research. This work establishes an effective method for analyzing the nonlinear vibration of the irregular plate with various boundaries, which provides a new theoretical technique for the dynamic design of the complex geometric structures in the aerospace field.