Nonlinear vibration of nanobeams under electrostatic force based on the nonlocal strain gradient theory

The nonlinear vibration of a nanobeam under electrostatic force is investigated through the nonlocal strain gradient theory. Using Galerkin method, the partial differential equation of motion is reduced to an ordinary nonlinear differential one. The equivalent linearization method with a weighted av...

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Bibliographic Details
Published in:International journal of mechanics and materials in design 2020-06, Vol.16 (2), p.289-308
Main Authors: Dang, Van-Hieu, Nguyen, Dong-Anh, Le, Minh-Quy, Duong, The-Hung
Format: Article
Language:English
Subjects:
Characterization and Evaluation of Materials
Classical Mechanics
Engineering
Engineering Design
Equations of motion
Galerkin method
Partial differential equations
Solid Mechanics
Strain
Vibration
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Summary:The nonlinear vibration of a nanobeam under electrostatic force is investigated through the nonlocal strain gradient theory. Using Galerkin method, the partial differential equation of motion is reduced to an ordinary nonlinear differential one. The equivalent linearization method with a weighted averaging and a variational approach are used independently to establish the frequency–amplitude relationship under closed-forms for comparison purpose. Effects of material and operational parameters on the frequency ratio (the ratio of nonlinear frequency to linear frequency), on the nonlinear frequency, and on the stable configuration of the nanobeam are studied and discussed.
ISSN:1569-1713
1573-8841
DOI:10.1007/s10999-019-09468-8