Nonlocal free and forced vibration of a graded Timoshenko nanobeam resting on a nonlinear elastic foundation

M. Trabelssi, Sami El-Borgi, R. Fernandes, L. L. Ke

Research output: Contribution to journalArticle

Abstract

The free and forced vibration of a nonlocal Timoshenko graded nanobeam resting on a nonlinear elastic foundation is investigated in this paper. The Timoshenko beam theory along with the von Kármán geometric nonlinearity is formulated while accounting for Eringen's nonlocal elasticity differential model. A power-law distribution is used to model the material distribution along the beam thickness. The equations of motion are derived using Hamilton's principle and then solved analytically using the Method of Multiple Scale (MMS) and numerically using the Differential Quadrature Method (DQM) and the Harmonic Quadrature Method (HQM). The considered boundary conditions include both Hinged-Hinged and Clamped-Clamped. The obtained nonlocal nonlinear frequencies of the nanobeam are first validated based on published analytical results that use linear mode shapes. A frequency response analysis is also conducted utilizing both MMS and DQM. The time discretization in DQM solution is performed using Spectral Method (SPM) and HQM. The primary objective of this study is to investigate the effects of the nonlocal parameter, power-law index, linear and nonlinear stiffnesses of the elastic foundation as well as the boundary conditions on the dynamic response of the nanobeam.

LanguageEnglish
Pages331-349
Number of pages19
JournalComposites Part B: Engineering
Volume157
DOIs
Publication statusPublished - 15 Jan 2019

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Boundary conditions
Equations of motion
Frequency response
Dynamic response
Elasticity
Stiffness

Keywords

  • Differential quadrature method (DQM)
  • Functionally graded nanobeam
  • Harmonic quadrature method (HQM)
  • Method of multiple scales (MMS)
  • Nonlocal theory

ASJC Scopus subject areas

  • Ceramics and Composites
  • Mechanics of Materials
  • Mechanical Engineering
  • Industrial and Manufacturing Engineering

Cite this

Nonlocal free and forced vibration of a graded Timoshenko nanobeam resting on a nonlinear elastic foundation. / Trabelssi, M.; El-Borgi, Sami; Fernandes, R.; Ke, L. L.

In: Composites Part B: Engineering, Vol. 157, 15.01.2019, p. 331-349.

Research output: Contribution to journalArticle

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