Vibration analysis of viscoelastic single-walled carbon nanotubes resting on a viscoelastic foundation

Abstract

Vibration responses are investigated for a viscoelastic single-walled carbon nanotube (visco-SWCNT) resting on a viscoelastic foundation. Based on the nonlocal Euler-Bernoulli beam model, velocity-dependent external damping and Kelvin viscoelastic foundation model, the governing equations are derived. The transfer function method (TFM) is then used to compute the natural frequencies for general boundary conditions and foundations. In particular, the exact analytical expressions of both complex natural frequencies and critical viscoelastic parameters are obtained for the Kelvin-Voigt visco-SWCNTs with full foundations and certain boundary conditions, and several physically intuitive special cases are discussed. Substantial nonlocal effect, the influence of geometric and physical parameters of the SWCNT and the viscoelastic foundation are observed for the natural frequencies of the supported SWCNTs. The study demonstrates the efficiency and robustness of the developed model for the vibration of the visco-SWCNT-viscoelastic foundation coupling system.

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