Internal resonance of an axially transporting beam with a two-frequency parametric excitation

doi:10.1007/s10483-022-2930-9

Abstract

Abstract: This paper investigates the transverse 3:1 internal resonance of an axially transporting nonlinear viscoelastic Euler-Bernoulli beam with a two-frequency parametric excitation caused by a speed perturbation. The Kelvin-Voigt model is introduced to describe the viscoelastic characteristics of the axially transporting beam. The governing equation and the associated boundary conditions are obtained by Newton’s second law. The method of multiple scales is utilized to obtain the steady-state responses. The Routh-Hurwitz criterion is used to determine the stabilities and bifurcations of the steady-state responses. The effects of the material viscoelastic coefficient on the dynamics of the transporting beam are studied in detail by a series of numerical demonstrations. Interesting phenomena of the steady-state responses are revealed in the 3:1 internal resonance and two-frequency parametric excitation. The approximate analytical method is validated via a differential quadrature method.

Key words: axially transporting viscoelastic beam, internal resonance, two-frequency excitation, nonlinear vibration, perturbation technique

2010 MSC Number:

70K28

Dengbo ZHANG, Youqi TANG, Ruquan LIANG, Yuanmei SONG, Liqun CHEN. Internal resonance of an axially transporting beam with a two-frequency parametric excitation. Applied Mathematics and Mechanics (English Edition), 2022, 43(12): 1805-1820.

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