Nonlinear dynamic response and phase‐plane analysis of imperfect functionally graded CNT‐reinforced magneto–electro–elastic sandwich panels under thermo–hygro–mechanical loads

Abstract This paper establishes an enhanced analytical framework for capturing the nonlinear dynamic behavior and phase‐plane evolution of functionally graded carbon‐nanotube‐reinforced magneto–electro–elastic (FG‐CNT/MEE) sandwich panels operating under simultaneous mechanical, thermal, electrical, magnetic, and hygro–mechanical actions. The proposed multifunctional panel consists of two MEE face sheets and a CNT‐reinforced nanocomposite core, in which the nanotube content is distributed according to several functional gradation patterns (FG‐O, FG‐V, and FG‐X) to tailor stiffness and electromechanical coupling. The governing equations are rigorously derived using Reddy's higher‐order shear deformation theory (HSDT) in conjunction with Hamilton's principle, incorporating the synergistic influences of temperature rise, moisture diffusion, electromagnetic potentials, geometric imperfections, and Pasternak‐type foundation parameters. A combined Bubnov–Galerkin reduction and fourth‐order Runge–Kutta time‐integration scheme is employed to efficiently track transient nonlinear responses. The parametric study reveals several important physical trends. Hygrothermal environments strongly soften the structure, causing pronounced frequency reductions and amplified nonlinear deflections, while elastic foundations exert a dominant stiffening effect that effectively suppresses vibration amplitudes. Notably, the FG‐X CNT distribution consistently outperforms other patterns in terms of vibrational stability due to its optimized stiffness gradient, and increasing thermal loads drive phase‐plane trajectories toward weakly stable, high‐energy oscillatory regimes. The proposed framework offers a robust and computationally efficient tool for predicting, assessing, and optimizing the nonlinear dynamic performance of advanced CNT/MEE sandwich structures. The findings provide important design guidelines for aerospace, defense, and civil engineering components intended to function in harsh thermo–electro–magneto–mechanical environments.