Abstract
Present paper deals with the vibration analysis of nano plate supported by Winkler foundation using Eringen’s elasticity theory with Classical Plate theory. Rayleigh-Ritz method has been employed in this study for finding frequencies of plate subjected to different edge conditions. The obtained results are first tested for convergence and then validated with the published literature. Further study is carried out to analyse the effect of various parameters on natural nondimensional frequencies of nano plate resting on Winkler foundation. The study reveals that the non-local effect has significant effect on vibration behaviour of nano plate resting on elastic foundation. Observations shows that on increasing the Winkler foundation modulus and aspect ratio the nondimensional frequency parameters increases.
Highlights
Nanoplates are the building blocks for various nanoscale objects which are called nanostructures
The frequency parameter of nano plates is analysed in detail
Convergence of frequency parameter of nano plate subjected to various boundary conditions is shown in Fig. 2 with respect to different number of the polynomials
Summary
Nanoplates are the building blocks for various nanoscale objects which are called nanostructures. Nonlocal Continuum mechanics theory put forward by Eringen [7] incorporates small length scale effect which plays a key role when Nano structures are taken into account. This theory is a widely used as results are found to be an accurate and quick analysis of Nano plates can be done. Natrajan et al [8] analysed the size effect on linear free vibration behaviour of nano plate using Erigen’s nonlocal elasticity theory. The extant literature review suggests that no study highlights in detail, the effect of various material and foundation parameters on Nano plates resting on elastic support subjected to different combinations of boundary conditions
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