Free Vibrations of FG-GPLRC Magneto–Electro–Elastic Sandwich Cantilevered Trapezoidal Plates with Variable Thickness

This paper introduces a comprehensive methodology for the investigation of free vibrations in intelligent composite constructions. The design integrates a functionally graded graphene platelet-reinforced composite (FG-GPLRC) core with magnetoelastic faculae composed of BaTiO 3 –CoFe 2 O 4 . Four GPL distributions within the FG-GPLRC core enhance its performance. Material characterization employs the enhanced Halpin–Tsai method, enabling precise computation of the composite’s properties. Coupling effects across elastic, thermal, electrical, and magnetic fields are elucidated. Nonlinear equations for controlling smart, gradient-thickness FG-GPLRC panels are derived using first-order shear deformation theory (FSDT) and Hamilton’s Principle. Natural frequencies are determined via double triangular series approximation and Galerkin’s method. A detailed parameter analysis investigates the influence of GPL on centration, distribution, temperature, trapezoid angles, base dimensions, and thickness on vibration modes and frequencies. Insights reveal how geometry, materials, and thickness gradients affect smart composite dynamics. The model’s accuracy is verified against finite element simulations, showcasing its utility for analyzing advanced composites under free vibration.