Acta Mechanica Solida Sinica

, Volume 30, Issue 4, pp 416–424 | Cite as

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

Article

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 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.

Keywords

Fractional calculus Viscoelastic nanobeam Nonlinear vibrations 

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Copyright information

© The Chinese Society of Theoretical and Applied Mechanics and Technology 2017

Authors and Affiliations

  1. 1.Department of Mechanical EngineeringUniversity of GuilanRashtIran

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