The nonlocal elasticity theory for geometrically nonlinear vibrations of double-layer nanoplate systems in magnetic field

Abstract

The geometrically nonlinear vibrations of simply supported double-layer graphene sheet systems under in-plane magnetic field are considered in the presented manuscript. The interaction between layers is taken into account due to van der Waals forces. The investigation is based on the nonlocal elasticity theory, Kirchhoff plate theory and von Kármán theory. The effect of the magnetic field is due to the Lorentz force based on Maxwell’s equations. The governing equations are used in mixed form by introducing the stress Airy function. The analytical presentation of the nonlinear frequency ratio for in-phase vibration and anti-phase vibration modes is presented. It is shown that the nonlocal parameter in the compatibility equation can significantly change the vibration characteristics.