In this study, the large amplitude free vibration of nanobeams based on the modified couple stress theory was developed by using Total Lagrangian finite element formulation. In this study, Timoshenko beam theory has been used in free vibration analysis of nanobeams. Minimal kinematic assumptions have been used to model nanobeams. With this model, free vibration of nanobeams with small to large amplitude and with arbitrary boundary conditions can be analyzed. The numerical results obtained for free vibration based on the modified couple stress theory with small amplitude and the results obtained for free vibration with large amplitude without considering the modified couple stress theory are in good agreement with the similar results reported in previous research. Effects of the dimensionless length scale parameter, slenderness ratio, vibration amplitude and different boundary conditions on the nonlinear frequency ratio of nanobeams have been investigated. The results show the importance of considering nonlinear and size effects in the free vibration analysis of nanobeams with large amplitude.

中文翻译：

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基于修正耦合应力理论的纳米梁大振幅自由振动分析

在这项研究中，基于修正耦合应力理论的纳米梁的大振幅自由振动是利用总拉格朗日有限元公式开发的。在这项研究中，Timoshenko 梁理论已被用于纳米梁的自由振动分析。最小运动学假设已用于模拟纳米束。使用该模型，可以分析具有小到大振幅和任意边界条件的纳米束的自由振动。基于修正的小振幅耦合应力理论得到的自由振动数值结果和不考虑修正耦合应力理论的大振幅自由振动得到的结果与先前研究报道的类似结果非常吻合。无量纲长度尺度参数、长细比的影响，研究了振动幅度和不同边界条件对纳米束非线性频率比的影响。结果表明在大振幅纳米梁的自由振动分析中考虑非线性和尺寸效应的重要性。