The Free Vibration Analysis of Nonlocal SLGS Based on Various Plate Theories under Magnetic Field

چکیده مقاله

In this article, the nonlocal natural frequency of single layer nano graphene sheet using various plate theories is presented. SLGS is separately subjected to magnetic fields in x, y and z directions. Various plate theories including classic plate (CPT), first order shear deformation (FSDT), third order shear deformation (TSDT), Ambartsumain, Reissner, Touratier, Aydogdu theories are used in this article. The equations of motion for the nonlocal SLGS are derived using Hamilton's principle. Navier’s solution is employed to obtain the nonlocal natural frequencies of SLGS. Compression between various plate theories showed that the results of Reissner plate theory is very closer to the obtained FSDT results and also the results of Touratier and Aydogduplate theories is coincident with TSDT results. The nonlocal natural frequenciy of single layer graphene sheet (SLGS) increases with an increase in the magnetic fields. Effect of magnetic field in z direction on the nonlocal natural frequencies of SLGS is higher than the effects of magnetic fields in x and y directions. Influence of magnetic field on the higher nonlocal natural frequencies is higher than that of for the lower nonlocal natural frequencies. Influence of magnetic fields on the nonlocal natural frequencies for Aydogdu and TSDT is higher than that of other plate theories.