Free vibration of hinged FG-GPLRC magneto-electro-elastic variable-thickness folded trapezoidal sandwich panels

This study presents an integrated approach to investigate the free vibration characteristics of variable-thickness, seamless, hinge-folded trapezoidal sandwich panels with magneto-electro-elastic face sheets and a functionally graded graphene platelet-reinforced composite core. The design leverages the excellent mechanical strength, high electrical conductivity, and lightweight properties of graphene, while considering multi-field coupling effects among elastic, thermal, electrical, and magnetic fields. The incorporation of hinge mechanisms significantly enhances structural flexibility and adaptability, enabling position-specific morphing under different operational conditions, thereby optimizing stress distribution and improving reliability. An enhanced Halpin-Tsai method is employed to accurately characterize composite material properties. Nonlinear equations are derived via the first-order shear deformation theory and Hamilton’s principle, comprehensively accounting for shear deformation, rotatory inertia, and providing a rigorous theoretical basis for motion equations. Double trigonometric series approximation combined with Galerkin’s method is used to calculate the natural frequencies. Through systematic analysis, the study reveals how key geometrical parameters, material properties, and thickness variations impact the intrinsic frequency. This work not only provides insights into the theoretical aspects of advanced smart composite structures but also provides practical guidelines for optimizing design parameters related to geometry, material selection, and thickness distribution. The proposed methodology offers potential applications in aerospace, micro-electromechanical systems, and other adaptive structural systems.

本研究提出一种集成研究方法，用于探究具备磁电弹性面板(magneto-electro-elastic face sheets)与功能梯度石墨烯片增强复合芯层(functionally graded graphene platelet-reinforced composite core)的变厚度无缝铰链折叠梯形夹芯板的自由振动特性。该设计充分利用石墨烯优异的力学强度、高导电性与轻质特性，同时兼顾弹性场、热场、电场与磁场之间的多场耦合效应。铰链结构的引入显著提升了结构的灵活性与适配性，可在不同工况下实现位置特异性的形态变形，进而优化应力分布并提升结构可靠性。研究采用改进型Halpin-Tsai模型(Halpin-Tsai method)以精准表征复合材料的力学性能。基于一阶剪切变形理论与哈密顿原理(Hamilton’s principle)推导得到非线性控制方程，全面考虑剪切变形与转动惯量效应，为运动方程构建了严谨的理论基础。采用双重三角级数近似结合伽辽金法(Galerkin’s method)求解结构固有频率。通过系统性参数分析，本研究揭示了关键几何参数、材料属性与厚度变化对结构固有频率的影响规律。本工作不仅为先进智能复合结构的理论研究提供了全新视角，同时为几何设计、材料选型与厚度分布相关的参数优化提供了切实可行的指导。所提出的研究方法可在航空航天、微机电系统(Micro-Electro-Mechanical Systems, MEMS)及其他自适应结构系统中展现出潜在应用价值。