Free Vibration Analysis of Non-Uniform Circular Nanoplate

In this paper, axisymmetric free vibration analysis of a circular Nano-plate having variable thickness was studied. The variation in thickness of plate was considered as a linearly in radial direction. Nonlocal elasticity theory was utilized to take into account size-dependent effects. Ritz functions was utilized to obtain the frequency equations for simply supported and clamped boundary. To verify accuracy of Ritz method, differential transform method (DTM) also used to drive the size dependent natural frequencies of circular nano-plates. The validity of solutions was performed by comparing present results with those of the literature for both classical plate and nano plate. Effect of nonlocal parameter, mode number and taper parameter on the natural frequency are investigated. Results showed that taper parameter has significant effect on the non-dimensional frequency and its effects on the clamped boundary condition is more than simply support.

Keywords:

Nonlocal theory , Axisymmetric vibration , Variable thickness plate , Ritz method , Differential transform method