Transverse non-linear forced vibration of axially moving viscoelastic beam with an internal resonance

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Journal of Vibration and Shock ›› 2017, Vol. 36 ›› Issue (17) : 69-73.

Huang Ling-lu1, Mao Xiao-ye1, DING Hu1, Chen Li-qun1,2

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Abstract

The transverse nonlinear forced vibration of axially moving viscoelastic beams with a three-to-one internal resonance is analytically and numerically studied in this paper. The material obeys the kelvin model in which the material derivative is taken part in the viscoelastic constitution relation instead of the simple partial time derivative. For the first time, the method of multiple scales is developed to present the governing partial differential equations of motion for the continuous system. The solvability condition of nonlinear forced vibration in the transverse motion is derived under the internal resonance. The steady-state response and stable boundary are determined. The effects of the system parameters on the steady-state response are examined. The approximate analytical outcomes are qualitatively and quantitatively supported by the numerical simulations.

Key words

Axially moving beam / internal resonance / forced vibration / multi-scale method

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Huang Ling-lu1, Mao Xiao-ye1, DING Hu1, Chen Li-qun1,2. Transverse non-linear forced vibration of axially moving viscoelastic beam with an internal resonance[J]. Journal of Vibration and Shock, 2017, 36(17): 69-73

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