Wave propagation analysis of embedded single-layered graphene sheets subjected to a longitudinal magnetic field

Present paper aims to investigate the behavior of the waves propagating through a single-layered graphene sheet (SLGS) in the attendance of a longitudinal magnetic field. The generated force which is induced to the graphene sheet by magnetic field is calculated by developing the Maxwell s equation for SLGSs in the x direction. Furthermore, a nonlocal strain gradient theory (NSGT) is exploited to procure more reliable results by considering the stiffness-hardening effect in addition to the stiffness-softening one. Kinematic relations are derived in the framework of a refined trigonometric two-variable plate theory which makes the analysis needless of any shear correction factor. Employing the Hamilton s principle, the Euler-Lagrange equations are derived and by incorporating these equations with the nonlocal constitutive relations of the NSGT the governing equations are derived in terms of displacement fields. The final Eigenvalue problem is supposed to be solved and the wave frequency and phase velocity values are derived. Moreover, validation procedure is performed by comparing the presented results with those of former attempts made by other researchers. At last, effect of each parameter is magnified in detail by plotting various diagrams for those parameters

Keywords:

Wave propagation , Single-layered graphene sheet (SLGS) , Nonlocal strain gradient theory (NSGT) , Winkler-Pasternak foundation , Longitudinal magnetic field , Refined-trigonometric two-variable plate theory