Torsional vibration of cracked carbon nanotubes with torsional restraints using Eringen's nonlocal differential model

YAYLI M. Ö., YEREL KANDEMİR S., ÇERÇEVİK A. E.

JOURNAL OF LOW FREQUENCY NOISE VIBRATION AND ACTIVE CONTROL, vol.38, no.1, pp.70-87, 2019 (SCI-Expanded) identifier identifier

  • Publication Type: Article / Article
  • Volume: 38 Issue: 1
  • Publication Date: 2019
  • Doi Number: 10.1177/1461348418813255
  • Journal Name: JOURNAL OF LOW FREQUENCY NOISE VIBRATION AND ACTIVE CONTROL
  • Journal Indexes: Science Citation Index Expanded (SCI-EXPANDED), Scopus
  • Page Numbers: pp.70-87
  • Keywords: Torsional vibration, cracked carbon nanotubes, Fourier sine series, deformable boundary conditions, BUCKLING ANALYSIS, STRESS GRADIENT, AXIAL VIBRATION, ELASTICITY, CONTINUUM, STRAIN, BEAMS, MICROTUBULES, NANOBEAMS, FREQUENCY
  • Bursa Uludag University Affiliated: Yes

Abstract

Free torsional vibration of cracked carbon nanotubes with elastic torsional boundary conditions is studied. Eringen's nonlocal elasticity theory is used in the analysis. Two similar rotation functions are represented by two Fourier sine series. A coefficient matrix including torsional springs and crack parameter is derived by using Stokes' transformation and nonlocal boundary conditions. This useful coefficient matrix can be used to obtain the torsional vibration frequencies of cracked nanotubes with restrained boundary conditions. Free torsional vibration frequencies are calculated by using Fourier sine series and compared with the finite element method and analytical solutions available in the literature. The effects of various parameters such as crack parameter, geometry of nanotubes, and deformable boundary conditions are discussed in detail.