Vibration analysis of a viscoelastic graphene sheet exposed to an in-plane magnetic field using the nonlocal strain gradient theory

Based on the nonlocal strain gradient theory, the transverse vibration of a viscoelastic graphene sheet subjected to an in-plane magnetic field and external forces is studied. A general governing equation for the graphene sheet vibration is formulated. Theoretical solutions for undamped and damped vibrational frequencies are obtained. The influence of the in-plane magnetic field on the damping ratio and on the frequencies of the free and forced vibrations is studied within the framework of the nonlocal strain gradient theory.