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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| Published in | Acta mechanica solida Sinica Vol. 30; no. 4; pp. 416 - 424 |
|---|---|
| Main Authors | , , |
| Format | Journal Article |
| Language | English |
| Published |
Singapore
Elsevier Ltd
01.08.2017
Springer Singapore |
| Subjects | |
| Online Access | Get full text |
| ISSN | 0894-9166 1860-2134 |
| DOI | 10.1016/j.camss.2017.07.003 |
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| Abstract | 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. |
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| AbstractList | 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 predictor—corrector method. Finally, the effects of initial displacement, fractional derivative order, vis-coelasticity coefficient, surface parameters and thickness-to-length ratio on the nonlinear time response of simply-supported and clamped-free silicon viscoelastic nanobeams are investigated. 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. 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 predictor–corrector 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. |
| Author | M. Faraji Oskouie;R. Ansari;F. Sadeghi |
| AuthorAffiliation | Department of Mechanical Engineering, University of Guilan, P.O. Box 3756, Rasht, Iran |
| Author_xml | – sequence: 1 givenname: M. Faraji surname: Oskouie fullname: Oskouie, M. Faraji – sequence: 2 givenname: R. surname: Ansari fullname: Ansari, R. email: r_ansari@guilan.ac.ir – sequence: 3 givenname: F. surname: Sadeghi fullname: Sadeghi, F. |
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| Keywords | Nonlinear vibrations Viscoelastic nanobeam Fractional calculus |
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| Notes | 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. |
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| Snippet | The nonlinear vibrations of viscoelastic Euler-Bernoulli nanobeams are studied using the fractional calculus and the Gurtin-Murdoch theory. Employing... The nonlinear vibrations of viscoelastic Euler–Bernoulli nanobeams are studied using the fractional calculus and the Gurtin–Murdoch theory. Employing... The nonlinear vibrations of viscoelastic Euler—Bernoulli nanobeams are studied using the fractional calculus and the Gurtin—Murdoch theory. Employing... |
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| SubjectTerms | 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 |
| Title | Nonlinear vibration analysis of fractional viscoelastic Euler-Bernoulli nanobeams based on the surface stress theory |
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