Nonlinear vibrations of graphene nanoplates with arbitrarily orientated crack located in magnetic field using nonlocal elasticity theory

Abstract

Purpose The study explores frequency curves and natural frequencies as functions of crack length, crack angle, magnetic field strength and small size effects under the three boundary conditions. Design/methodology/approach This study investigates the nonlinear dynamics of a single-layered graphene nanoplate with an arbitrarily oriented crack under the influence of a magnetic field. The research focuses on three boundary conditions: simply supported, clamped and clamped-simply supported. The crack effect is modeled by incorporating membrane forces and additional flexural moments created by the crack into the equation of motion. Findings Results reveal that increasing the crack length, small size effects and magnetic field intensity reduces the flexural stiffness of the nanoplate, increases the compressive load and lowers its natural frequency. Additionally, excessive magnetic field intensity may lead to static buckling. The critical dimensionless magnetic fields are found to be 33.6, 95.1 and 72.3 for All edges of the nanoplate are simply supported (SSSS), fully clamped edges (CCCC) and two opposite edges are clamped and the other are simply supported (CSCS) nanoplates, respectively. Furthermore, for SSSS and CCCC boundary conditions, an increase in the crack angle results in a softening behavior of the hard spring. In contrast, the SCSC boundary condition exhibits the opposite behavior. These findings emphasize the importance of considering the effects of angled cracks and electromagnetic loads in the analysis and design of graphene-based nanostructures. Originality/value Novel equations are derived to account for the applied loads induced by the magnetic field. The nonlinear equation of motion is discretized using the Galerkin technique, and its analytical response is obtained via the multiple time-scales perturbation technique.

Topics & Concepts