Vibration Analysis of a Rotating Nanoplate Using Nonlocal Elasticity Theory

The nanostructures under rotation have high promising future to be used in nano-machines, nano-motors and nano-turbines. They are also one of the topics of interests and it is new in designing of rotating nano-systems. In this paper, the scale-dependent vibration analysis of a nanoplate with consideration of the axial force due to the rotation has been investigated. The governing equation and boundary conditions are derived using the Hamilton’s principle based on nonlocal elasticity theory. The boundary conditions of the nanoplate are considered as free-free in y direction and two clamped-free (cantilever plate) and clamped-simply (propped cantilever) in x direction. The equations have been solved using differential quadrature method to determine natural frequencies of the rotating nanoplate. For validation, in special cases, it has been shown that the obtained results coincide with literatures. The effects of the nonlocal parameter, aspect ratio, hub radius, angular velocity and different boundary conditions on the first three frequencies have been investigated. Results show that vibration behavior of the rotating nanoplate with cantilever boundary condition is different from other boundary conditions.