Akbarshahi Amir, Rajabpour Ali, Ghadiri Majid, Barooti Mohammad Mostafa
Advanced Simulation and Computing Laboratory, Mechanical Engineering Department, Imam Khomeini International University, Qazvin, 34149-16818, Iran.
J Mol Model. 2019 May 1;25(5):141. doi: 10.1007/s00894-019-3996-5.
The Eringen's nonlocal elasticity theory is employed to examine the free vibration of a rotating cantilever single-layer graphene sheet (SLGS) under low and high temperature conditions. The governing equations of motion and the related boundary conditions are obtained through Hamilton's principle based on the first-order shear deformation theory (FSDT) of nanoplates. The generalized differential quadrature method (GDQM) is utilized to solve the nondimensional equations of motion. The molecular dynamics (MD) simulation is conducted, and fundamental frequencies of the rotating cantilever square SLGS are computed using the fast Fourier transform (FFT). The comparison of MD and GDQM results leads to finding the appropriate value of the nonlocal parameter for the first time. As an interesting result, this value of the nonlocal parameter is independent of the angular velocity. Results indicate that increases in various parameters, such as the angular velocity, hub radius, nonlocal parameter, and temperature changes in low temperature conditions, leads the first and the second frequencies to increase. In addition, it can be seen that the influence of the hub radius or nonlocal parameters on frequencies cannot be ignored in high angular velocities. Moreover, it is not possible to neglect the angular velocity or nonlocal parameter in high hub radius. The results show that the influence of parameters such as setting angle or nonlocal parameter on the first and the second frequencies increases when some parameters increase, such as the angular velocity, hub radius or temperature change. Graphical abstract (a) A schematic of a rotating cantilever nanoplate. (b) A schematic of cantilever armchair SLGS simulated by MD.
采用埃林根的非局部弹性理论研究旋转悬臂单层石墨烯片（SLGS）在低温和高温条件下的自由振动。基于纳米板的一阶剪切变形理论（FSDT），通过哈密顿原理得到运动控制方程和相关边界条件。利用广义微分求积法（GDQM）求解无量纲运动方程。进行分子动力学（MD）模拟，并使用快速傅里叶变换（FFT）计算旋转悬臂方形SLGS的基频。MD和GDQM结果的比较首次得出了非局部参数的合适值。一个有趣的结果是，该非局部参数值与角速度无关。结果表明，在低温条件下，各种参数的增加，如角速度、轮毂半径、非局部参数和温度变化，会导致第一和第二频率增加。此外，可以看出，在高角速度下，轮毂半径或非局部参数对频率的影响不可忽略。而且，在高轮毂半径下，角速度或非局部参数也不能忽略。结果表明，当一些参数增加时，如角速度、轮毂半径或温度变化，设置角度或非局部参数等参数对第一和第二频率的影响会增加。图形摘要（a）旋转悬臂纳米板示意图。（b）MD模拟的悬臂扶手椅形SLGS示意图。
