Magneto-hygro-thermal vibration behavior of elastically coupled nanoplate systems incorporating nonlocal and strain gradient effects

Magneto-hygro-thermal vibration analysis of double-layered nanoplates made of functionally graded materials is presented based on higher order refined plate theory. For the first time, a double-layered nanoplate is modeled via nonlocal strain gradient theory in which both stiffness-softening and stiffness-hardening effects are incorporated. Another novelty of this paper is that the effects of magnetic and hygro-thermal fields on inhomogeneous double-layered nanoplates are considered to study their behavior under different physical fields. The gradation of material properties is considered using power-law model. The governing equations and related classical and non-classical boundary conditions are derived based on Hamilton’s principle. These equations are solved for hinged nanoplates via Galerkin’s method. It is indicated that type of vibration, moisture rise, temperature rise, nonlocal parameter, strain gradient parameter, material gradation, elastic foundation and side-to-thickness have a remarkable influence on vibration behavior of double-layered nanoscale plates.