The free vibration of single-layered graphene sheet (SLGS) has been studied by nonlocal modified couple stress theory (NMCS), analytically. Governing equation of motion for SLGS is obtained via thin plate theory in conjunction with Hamilton’s principle for two cases: (1) using nonlocal parameter only for stress tensor, (2) using nonlocal parameter for both stress and couple stress tensors. Navier’s approach has been used to solve the governing equations for simply supported boundary conditions. It is found that the frequency ratios decrease with increasing nonlocal parameter and also with enhancing vibration modes, but increase with raising length scale parameter. The nonlocal and length scale parameters are more prominent in higher vibration modes. The obtained results have been compared with the previous studies obtained by using classical plate theory, the modified couple stress theory and nonlocal elasticity theory, separately.

中文翻译：

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使用非局部修正耦合应力理论测定单层石墨烯片的振动

单层石墨烯片（SLGS）的自由振动已经通过非局部修正耦合应力理论（NMCS）进行了分析研究。SLGS 的控制运动方程是通过薄板理论结合 Hamilton 原理在两种情况下获得的：(1) 仅对应力张量使用非局部参数，(2) 对应力和耦合应力张量都使用非局部参数。Navier 的方法已被用于求解简支边界条件的控制方程。发现频率比随着非局部参数的增加和振动模式的增加而降低，但随着长度尺度参数的增加而增加。非局部和长度尺度参数在较高的振动模式下更为突出。