Free vibration and nonlinear dynamic behaviors of the imperfect smart electric magnetic FG-laminated composite panel in a hygrothermal environments

Piezoelectric and piezomagnetic layers are known to enhance material properties and increase load capacity. However, most studies focused on the effects of mechanical and thermal loads on these structures. This work aimed to investigate the complex external condition of uniformed load, thermal load, moisture parameter and electric–magnetic potentials of the smart electric magnetic panel using an analytical approach. The core of the panel is made of graphene platelets, and the two outer layers consist of barium titanate (BaTiO 3 ) and cobalt ferric oxide (CoFe 2 O 4 ). The Ready’s first-order shear deformation and Hamilton’s theory are proposed to govern the basic equation. After that, the stress function is introduced, and then apply the Galerkin method to determine the natural frequency and dynamic response of the panel. The final chapter analyzes the relationship between the natural frequency and amplitude of the electromagnetic panel with simplified assumptions. The numerical results are highlighted using the Runge–Kutta method, including the influence of the piezoelectric outer layer, geometry parameters, imperfection, elastic foundations, graphene volume fraction, thermal loads and electric and magnetic fields of the electromagnetic panel. The reliability of this computational theory is validated by other publications. In addition, the new influence of electrical and magnetic field parameters on the panel’s natural frequency is also emphasized.