Free longitudinal vibration of a nanorod with elastic spring boundary conditions made of functionally graded material


YAYLI M. Ö.

MICRO & NANO LETTERS, vol.13, no.7, pp.1031-1035, 2018 (Peer-Reviewed Journal) identifier identifier

  • Publication Type: Article / Article
  • Volume: 13 Issue: 7
  • Publication Date: 2018
  • Doi Number: 10.1049/mnl.2018.0181
  • Journal Name: MICRO & NANO LETTERS
  • Journal Indexes: Science Citation Index Expanded, Scopus
  • Page Numbers: pp.1031-1035
  • Keywords: vibrations, elasticity, functionally graded materials, nanorods, nanomechanics, eigenvalues and eigenfunctions, finite element analysis, free longitudinal vibration, elastic spring boundary conditions, functionally graded material, dynamical analysis, functionally graded nanorods, longitudinal vibration analysis, FG restrained nanorods, nonlocal elasticity theory, nonlocal differential relations, coefficient matrix, exact eigenvalue method, finite-element method, nonlocal parameter, boundary conditions, axial frequencies, STRAIN GRADIENT ELASTICITY, FINITE-ELEMENT-METHOD, NONLOCAL ELASTICITY, BUCKLING ANALYSIS, CARBON NANOTUBES, NANOSTRUCTURES, FOUNDATION, TORSION, BEAMS

Abstract

The elastic spring boundary conditions play an important role in dynamical analysis of functionally graded (FG) nanorods. However, these special issues have not been properly paid attention to in the previously developed non-local models. In this work, longitudinal vibration analysis of FG restrained nanorods is presented via non-local elasticity theory. Two axial springs are attached to a FG nanorod at both ends. By considering the non-local differential relations for the FG nanorod, a coefficient matrix is derived and analysed via an exact eigenvalue method. Finally, the results calculated from finite-element method are used to validate the present method. The influence of FG index, non-local parameter and boundary conditions on the axial frequencies of FG nanorods is discussed.