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. interaction between layers is taken into account due to van der Waals forces. investigation based on nonlocal elasticity theory, Kirchhoff plate theory and von Kármán theory. effect Lorentz force Maxwell’s equations. governing equations used mixed form by introducing stress Airy function. analytical presentation frequency ratio for in-phase vibration anti-phase modes presented. It shown that parameter compatibility equation can significantly change characteristics.