Nonlinear chaotic dynamics analysis of magneto-electro-elastic laminated nanoplates considering flexomagnetoelectric effect in hygrothermal environments

This paper presents the nonlinear chaotic mechanical model for magneto-electric elastic (MEE) laminated nanoplates, with the flexomagnetoelectric (FME) effect, subjected to multi-physical field excitation. Utilizing the high-order shear deformation theory (HSDT), Hamilton’s principle, and the nonlinear strain-displacement relationships from von Karman’s theory, the governing nonlinear equations for the system are derived. The application of the nonlocal strain gradient theory (NSGT) facilitates the consideration of the size effect in the system. The employment of the Airy stress function manages the nonlinear-nonlocal terms in the control equation. The accurate solution approach is ultimately formulated by combining the dual-mode Galerkin method with the fourth-order Runge-Kutta method. The outcomes indicate that the nonlinear chaotic behavior of MEE laminated nanoplates is substantially affected by the FME effect, hygrothermal conditions, and electromagnetic field. The research conducted in this paper intends to offer the comprehensive theoretical basis for the utilization of MEE nanomaterials in industrial engineering, alongside the derivation of criteria essential for mitigating and controlling the nonlinear chaotic behaviors within the system.