Dynamic and pull-in instability analyses of functionally graded nanoplates via nonlocal strain gradient theory

The main subject of this study is the dynamic and static pull-in analyses of rectangular nanoplates made of functionally graded materials based on the nonlocal strain gradient theory compared with the strain gradient theory, Eringen's differential method, and classical theory considering dispar...

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Published inMechanics based design of structures and machines Vol. 50; no. 2; pp. 588 - 608
Main Authors Torabi, Jalal, Ansari, Reza, Zabihi, Ali, Hosseini, Kamyar
Format Journal Article
LanguageEnglish
Published Taylor & Francis 31.01.2022
Subjects
Dynamic and static pull-in
FG rectangular plate
homotopy analysis method
nonlocal strain gradient theory
omitting secular terms
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ISSN1539-7734
1539-7742
DOI10.1080/15397734.2020.1721298

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Abstract The main subject of this study is the dynamic and static pull-in analyses of rectangular nanoplates made of functionally graded materials based on the nonlocal strain gradient theory compared with the strain gradient theory, Eringen's differential method, and classical theory considering disparate boundary conditions (BCs). To this end, the governing equation is derived based on Kirchhoff's plate theory and then, the Galerkin method is implemented to arrive at an ordinary differential equation of second-order in the time domain. The homotopy analysis method is used as an analytical solution methodology to solve the nonlinear ordinary differential equation which is under different nonlinear forces such as intermolecular, electrostatic and hydrostatic one. Likewise, an efficient technique is exerted for omitting secular terms. Accordingly, the dynamic pull-in voltage is obtained for different non-classical continuum theories, material gradient indices, nonlocal parameters and internal length scale parameters. The dynamic and static pull-in instabilities are also compared in the same situation. Additionally, the effects of the nonlocal parameter and internal length scale parameter on the non-dimensional frequency against the initial amplitude, electrostatic force and hydrostatic actuation are explored in disparate boundary conditions. Communicated by Eleonora Tubaldi.
AbstractList The main subject of this study is the dynamic and static pull-in analyses of rectangular nanoplates made of functionally graded materials based on the nonlocal strain gradient theory compared with the strain gradient theory, Eringen's differential method, and classical theory considering disparate boundary conditions (BCs). To this end, the governing equation is derived based on Kirchhoff's plate theory and then, the Galerkin method is implemented to arrive at an ordinary differential equation of second-order in the time domain. The homotopy analysis method is used as an analytical solution methodology to solve the nonlinear ordinary differential equation which is under different nonlinear forces such as intermolecular, electrostatic and hydrostatic one. Likewise, an efficient technique is exerted for omitting secular terms. Accordingly, the dynamic pull-in voltage is obtained for different non-classical continuum theories, material gradient indices, nonlocal parameters and internal length scale parameters. The dynamic and static pull-in instabilities are also compared in the same situation. Additionally, the effects of the nonlocal parameter and internal length scale parameter on the non-dimensional frequency against the initial amplitude, electrostatic force and hydrostatic actuation are explored in disparate boundary conditions. Communicated by Eleonora Tubaldi.
Author Torabi, Jalal
Zabihi, Ali
Hosseini, Kamyar
Ansari, Reza
Author_xml – sequence: 1
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  surname: Torabi
  fullname: Torabi, Jalal
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  fullname: Ansari, Reza
  organization: Department of Mechanical Engineering, University of Guilan
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  fullname: Zabihi, Ali
  organization: Department of Mechanical Engineering, Ahrar Institute of Technology & Higher Education
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  givenname: Kamyar
  surname: Hosseini
  fullname: Hosseini, Kamyar
  organization: Department of Mathematics, Rasht Branch, Islamic Azad University
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SubjectTerms Dynamic and static pull-in
FG rectangular plate
homotopy analysis method
nonlocal strain gradient theory
omitting secular terms
Title Dynamic and pull-in instability analyses of functionally graded nanoplates via nonlocal strain gradient theory
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