Ritz Method in Vibration Analysis for Embedded Single-Layered Graphene Sheets Subjected to In-Plane Magnetic Field

Abstract

Vibrations of single-layered graphene sheets subjected to a longitudinal magnetic field are considered. The Winkler-type and Pasternak-type foundation models are employed to reproduce the surrounding elastic medium. The governing equation is based on the modified couple stress theory and Kirchhoff–Love hypotheses. The effect of the magnetic field is taken into account due to the Lorentz force deriving from Maxwell’s equations. The developed approach is based on applying the Ritz method. The proposed method is tested by a comparison with results from the existing literature. The numerical calculations are performed for different boundary conditions, including the mixed ones. The influence of the material length scale parameter, the elastic foundation parameters, the magnetic parameter and the boundary conditions on vibration frequencies is studied. It is observed that an increase of the magnetic parameter, as well as the elastic foundation parameters, brings results closer to the classical plate theory results. Furthermore, the current study can be applied to the design of microplates and nanoplates and their optimal usage.

Nonlinear Static Bending and Forced Vibrations of Single-Layer MoS2 with Thermal Stress

“…Since monolayer graphene was first mechanically exfoliated from graphite in 2004 [1], its excellent physical, chemical, and mechanical properties have attracted extensive attention [2][3][4][5][6][7]. At the same time, the graphene-like two-dimensional (2D) transition metal dichalcogenides (TMDCs) have attracted widespread attention due to their single-layer characteristics and their excellent mechanical properties similar to those of graphene [8][9][10][11][12][13].…”