Open AccessFundamental frequency analysis of rectangular piezoelectric nanoplate under in‐plane forces based on surface layer, non‐local elasticity, and two variable refined plate hypotheses
Author(s) -
Jamali Leila,
Ghassemi Aazam
Publication year - 2018
Publication title -
micro and nano letters
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.25
H-Index - 31
ISSN - 1750-0443
DOI - 10.1049/mnl.2017.0429
Subject(s) - piezoelectricity , elasticity (physics) , mechanics , boundary layer , mathematical analysis , boundary value problem , residual stress , work (physics) , finite difference method , finite element method , materials science , classical mechanics , surface (topology) , plane (geometry) , mathematics , physics , geometry , composite material , thermodynamics
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.