Asymptotic frequencies of various damped nonlocal beams and plates

Y. Lei, S. Adhikari, T. Murmu, M.I. Friswell

Research output: Contribution to journalArticlepeer-review

15 Citations (Scopus)


A striking difference between the conventional local and nonlocal dynamical systems is that the later possess finite asymptotic frequencies. The asymptotic frequencies of four kinds of nonlocal viscoelastic damped structures are derived, including an Euler–Bernoulli beam with rotary inertia, a Timoshenko beam, a Kirchhoff plate with rotary inertia and a Mindlin plate. For these undamped and damped nonlocal beam and plate models, the analytical expressions for the asymptotic frequencies, also called the maximum or escape frequencies, are obtained. For the damped nonlocal beams or plates, the asymptotic critical damping factors are also obtained. These quantities are independent of the boundary conditions and hence simply supported boundary conditions are used. Taking a carbon nanotube as a numerical example and using the Euler–Bernoulli beam model, the natural frequencies of the carbon nanotubes with typical boundary conditions are computed and the asymptotic characteristics of natural frequencies are shown.
Original languageEnglish
Pages (from-to)94-101
Number of pages8
JournalMechanics Research Communications
Publication statusPublished - Dec 2014
Externally publishedYes


  • Asymptotic frequencies
  • Nonlocal elasticity
  • Euler-Bernoulli beam
  • Timoshenko beam
  • Kirchhoff plate
  • Mindlin plate
  • Damping
  • Viscoelastic


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