Influence of various setting angles on vibration behavior of rotating graphene sheet: continuum modeling and molecular dynamics simulation.

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.