Study on Natural Vibration Characteristics of FG-GPLRC Cantilever Trapezoidal Plates with Perovskite Surface Layer

This paper posits the wing as a cantilevered laminated trapezoidal plate structure and investigates the natural vibrations of a variable-thickness trapezoidal plate composed of a functional gradient graphene plate reinforced composite (FG-GPLRC) core layer sandwiched between multi-layer carbon fiber panels with a perovskite surface layer. The FG-GPLRC core layer exhibits a gradient distribution of four classes of graphene plate layers. The material properties are evaluated using an improved Halpin–Tsai model to ensure accurate calculation of composite physical parameters. The present study investigates the photo-electro-thermo-elastic model of the trapezoidal plate. The governing equations of the plate are derived within the framework of first-order shear deformation theory and Hamilton’s principle. The structural natural frequencies are solved using a double trigonometric series expansion and the Galerkin method. It is evident that numerical simulations yield the plate’s frequency curves and modal shapes, thereby unveiling intrinsic relationships between natural vibrations and parameters. The study comprehensively investigates the influence of factors such as GPL distribution patterns, ambient temperature, trapezoidal plate angle, substrate dimensions, thickness gradient variations, and electric field strength on modes and frequencies. The analysis results indicate how geometric configuration, material composition gradients, thickness variations, and electric field strength jointly affect the dynamic behavior of such composite structures. By comparing with results from existing literature, the reliability of the theoretical model is verified, fully demonstrating its effectiveness and applicability in analyzing the dynamic response of advanced composites under free vibration conditions.