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