Fundamental frequency analysis of rectangular piezoelectric nanoplate under in-plane forces based on surface layer, non-local elasticity, and two variable refined plate hypotheses

Leila Jamali; Aazam Ghassemi

Fundamental frequency analysis of rectangular piezoelectric nanoplate under in-plane forces based on surface layer, non-local elasticity, and two variable refined plate hypotheses

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Author(s): Leila Jamali^{1, 2} and Aazam Ghassemi^{1, 2}
- Affiliations: 1: Department of Mechanical Engineering, Najafabad Branch , Islamic Azad University , Najafabad , Iran ;
  2: Modern Manufacturing Technologies Research Center, Najafabad Branch , Islamic Azad University , Najafabad , Iran
Source: Volume 13, Issue 1, January 2018, p. 47 – 53
DOI: 10.1049/mnl.2017.0429 , Online ISSN 1750-0443

Received 14/06/2017, Accepted 28/07/2017, Revised 16/07/2017, Published 01/01/2018

Fundamental frequency analysis of rectangular piezoelectric nanoplates via the surface layer and non-local small-scale hypotheses is investigated in the present work. The piezoelectric nanoplate is under in-plane forces. The equilibrium governing of piezoelectric nanoplates is attained via the two variable refined plate hypothesis, and then the equations of motion are achieved utilising Hamilton's principle. To solve these equations, the finite difference method is employed. To verify the exactness of the finite difference method, the governing equations are tested by the Navier's solution. Numerical results show a good accuracy among the outcomes of the present work and some accessible cases in the literature. The numerical results show that for negative residual surface stress, as the boundary condition becomes stiffer the effect of surface layer increases, while for positive one that phenomenon is inverse.

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Fundamental frequency analysis of rectangular piezoelectric nanoplate under in-plane forces based on surface layer, non-local elasticity, and two variable refined plate hypotheses

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