Magnetic field and surface elasticity effects on thermal vibration properties of nanoplates

Thermal vibration properties of nanoplates are studied in the present work. The governing equations of motion for the nanoplate are derived from the fundamental principles with the consideration of Eringen's nonlocal elasticity theory. The effects of magnetic field and surface elasticity are also considered in the analysis. Different surface layers are considered over the nanoplate on upper and lower sides. From the present analysis, it is found that the presence of surface layers on nanoplate increases the natural frequency and stiffens the structure, whereas the magnetic field softens the nanoplate and reduces the natural frequency. Further the effects of nonlocal scale, mode number, surface layer strength, surface residual stress, inplane load parameter and thickness of the nanoplate are studied with respect to temperature parameter. The results presented in this manuscript can provide a useful guidance for the study and design of next generation of nanodevices that make use of the thermal vibration properties of a monolayer graphene as the primary element.