Surface effects on free vibration of piezoelectric functionally graded nanobeams using nonlocal elasticity
type: Item
instance of: scholarly article
title: Surface effects on free vibration of piezoelectric functionally graded nanobeams using nonlocal elasticity
zbMATH Open document ID: 1319.74009
author: Sh. Hosseini Hashemi
author: Iman Nahas
author: Mahmood Fakher
author: Reza Nazemnezhad
published in: Acta Mechanica
publication date: 2014-06-20T00:00:00Z
review text: The authors study surface effects, including surface elasticity, surface stress, and surface density as well as the piezoelectric field on the free vibrations of a functionally graded material (FGM) nanobeam using nonlocal elasticity. The simply supported FGM nanobeam is composed of two different materials at the top and the bottom surfaces integrated on each side of the bulk. The surface effects are investigated using the Euler-Bernoulli model and by considering the normal stress along the height of the nanobeam. A cubic variation of the normal stress is assumed, and the balance conditions between the nanobeam bulk and its surfaces are satisfied. Accordingly, the surface density is introduced into the governing equations of the nanobeam. The isotropy and constant piezoelectric properties are assumed, and any residual surface stresses in the bulk due to the surface tension are neglected. The bulk and surface elasticity moduli, mass density, and residual surface stress are assumed to vary in the thickness direction according to the power law distribution, whereas Poisson's ratio is taken to be constant. The variations of the normalized natural frequencies of the nanobeam versus various values of the gradient index, the voltage values of the piezoelectric field, the nanobeam length, and the mode number are obtained. It is concluded that the voltage values and the material properties are two main approaches to achieve the desired natural frequencies in the inverse dynamic problem.
Mathematics Subject Classification ID: 74F15
Mathematics Subject Classification ID: 74H45
Mathematics Subject Classification ID: 74K10
Mathematics Subject Classification ID: 74E05
zbMATH DE Number: 6305999
zbMATH Keywords: Euler-Bernoulli model
zbMATH Keywords: surface stress
zbMATH Keywords: surface density
zbMATH Keywords: normal stress
zbMATH Keywords: voltage
zbMATH Keywords: inverse dynamic problem
reviewed by: M. Cengiz Dökmeci
MaRDI profile type: Publication
full work available at URL: s00707-013-1014-z
OpenAlex ID: W2011326720
cites work: Asymptotic splitting in the three-dimensional problem of elasticity for non-homogeneous piezoelectric plates
cites work: Modelling of finite piezoelectric patches: comparing an approximate power series expansion theory with exact theory
cites work: Modelling of thin piezoelectric layers on plates
cites work: Single point vibration control for a passive piezoelectric Bernoulli-Euler beam subjected to spatially varying harmonic loads
cites work: On the influence of pyroelectricity upon thermally induced vibrations of piezothermoelastic plates
cites work: A Reissner-Mindlin-type plate theory including the direct piezoelectric and the pyroelectric effect
cites work: An electromechanically coupled theory for piezoelastic beams taking into account the charge equation of electrostatics.
cites work: Size-dependent longitudinal and transverse wave propagation in embedded nanotubes with consideration of surface effects
cites work: Size-dependent elastic properties of unidirectional nano-composites with interface stresses
cites work: Effects of high-order surface stress on buckling and resonance behavior of nanowires
cites work: Finite element analysis of resonant properties of silicon nanowires with consideration of surface effects
cites work: A continuum theory of elastic material surfaces
cites work: Addenda to our paper: A continuum theory of elastic material surfaces
cites work: Thin plate theory including surface effects
cites work: Buckling of circular/annular Mindlin nanoplates via nonlocal elasticity
cites work: Nonlocal elasticity effect on vibration of in-plane loaded double-walled carbon nanotubes
cites work: Analytical solutions for coupled tension-bending of nanobeam-columns considering nonlocal size effects
cites work: Size-dependent elastic behavior of FGM ultra-thin films based on generalized refined theory
cites work: A nonlocal beam theory for bending, buckling, and vibration of nanobeams
cites work: Nonlocal polar elastic continua
DOI: 10.1007/S00707-013-1014-Z
description: scientific article; zbMATH DE number 6305999