Nonlinear free vibration analysis of magneto-electro-elastic laminated nanoplates with flexomagnetoelectric effect in hygrothermal environments

Abstract Magnetoelectroelastic (MEE) materials, as smart composites consisting of piezoelectric and piezomagnetic phases, exhibit distinct phenomena: the piezoelectric phase generates a flexoelectric effect, and the piezomagnetic phase induces a flexomagnetic effect. Hence, understanding the influence of the flexomagnetoelectric (FME) effect on the mechanical characteristics of these materials during their application is crucial. This article investigates the nonlinear free oscillation response of MEE laminated nanoplates, considering the FME effect and elastic foundation, in hygrothermal environments. The derivation of the nonlinear dominant equations for the MEE laminated nanoplate with hydrothermal environments has been accomplished, grounded in the principles of Hamilton’s principle, nonlocal strain gradient theory (NSGT), and the higher-order shear deformation theory (HSDT). Employing the Airy stress function serves as a means to handle the complexities arising from the nonlinear nonlocal terms. Moreover, the control equations are tackled by a combined approach that incorporates both the two-step perturbation method (TPM) and the Lindstedt-Poincare perturbation method for their solution. The TPM can obviate the necessity for making hypotheses or conjectures concerning the configuration function. Specifically, the effects of FME effects, NSGT parameters, elastic foundation parameters, dimensional parameters of the nanoplate, and various physical field parameters on the nonlinear free oscillation properties of the MEE nanoplate are meticulously examined. The findings of this study demonstrate significant application potential in the fields of nanosensors, actuators, and energy harvesters.