Asymptotic Frequencies of Damped Nonlocal Beams and Plates

Y Lei (National University of Defence Technology, Changsha, China), S Adhikari (Swansea University), T Murmu (University of the West of Scotland) & MI Friswell (Swansea University)

Mechanics Research Communications, Vol. 62, December 2014, pp. 94-101

Abstract

A striking difference between the conventional local and nonlocal dynamical systems is that the latter 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.

Paper Availability

This material has been published in the Mechanics Research Communications, Vol. 62, December 2014, pp. 94-101, the only definitive repository of the content that has been certified and accepted after peer review. Copyright and all rights therein are retained by Elsevier.


Link to paper using doi: 10.1016/j.mechrescom.2014.08.002

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