Nonlinear vibration analysis of fractional viscoelastic Euler-Bernoulli nanobeams based on the surface stress theory

The nonlinear vibrations of viscoelastic Euler-Bernoulli nanobeams are studied using the fractional calculus and the Gurtin-Murdoch theory. Employing Hamilton＇s principle, the governing equation considering surface effects is derived. The fractional integro-partial differential governing equation is...

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Bibliographic Details
Published inActa mechanica solida Sinica Vol. 30; no. 4; pp. 416 - 424
Main Authors Oskouie, M. Faraji, Ansari, R., Sadeghi, F.
Format Journal Article
LanguageEnglish
Published Singapore Elsevier Ltd 01.08.2017
Springer Singapore
Subjects
Classical Mechanics
Engineering
Fractional calculus
Nonlinear vibrations
Surfaces and Interfaces
Theoretical and Applied Mechanics
Thin Films
Viscoelastic nanobeam
伯努利
分数阶微积分
应力理论
振动分析
粘弹性系数
纳米
表面效应
非线性振动
Nonlinear vibrations
Viscoelastic nanobeam
Fractional calculus
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ISSN0894-9166
1860-2134
DOI10.1016/j.camss.2017.07.003

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Summary:The nonlinear vibrations of viscoelastic Euler-Bernoulli nanobeams are studied using the fractional calculus and the Gurtin-Murdoch theory. Employing Hamilton＇s principle, the governing equation considering surface effects is derived. The fractional integro-partial differential governing equation is first converted into a fractional-ordinary differential equation in the time domain using the Galerkin scheme. Thereafter, the set of nonlinear fractional time-dependent equations expressed in a state-space form is solved using the predictorcorrector method. Finally, the effects of initial displacement, fractional derivative order, viscoelasticity coefficient, surface parameters and thickness-to-length ratio on the nonlinear time response of simply-supported and clamped-free silicon viscoelastic nanobeams are investigated.
Bibliography:Fractional calculus Viscoelastic nanobeam Nonlinear vibrations
42-1121/O3
The nonlinear vibrations of viscoelastic Euler-Bernoulli nanobeams are studied using the fractional calculus and the Gurtin-Murdoch theory. Employing Hamilton＇s principle, the governing equation considering surface effects is derived. The fractional integro-partial differential governing equation is first converted into a fractional-ordinary differential equation in the time domain using the Galerkin scheme. Thereafter, the set of nonlinear fractional time-dependent equations expressed in a state-space form is solved using the predictorcorrector method. Finally, the effects of initial displacement, fractional derivative order, viscoelasticity coefficient, surface parameters and thickness-to-length ratio on the nonlinear time response of simply-supported and clamped-free silicon viscoelastic nanobeams are investigated.
ISSN:0894-9166
1860-2134
DOI:10.1016/j.camss.2017.07.003