Quasi-Periodic and Periodic Vibration Responses of an Axially Moving Beam under Multiple-Frequency Excitation

Xinru Fang, Lingdi Huang, Zhimei Lou and Yuanbin Wang ()
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Xinru Fang: Department of Mathematics, Shaoxing University, Shaoxing 312000, China
Lingdi Huang: Department of Mathematics, Shaoxing University, Shaoxing 312000, China
Zhimei Lou: Department of Physics, Shaoxing University, Shaoxing 312000, China
Yuanbin Wang: Department of Mathematics, Shaoxing University, Shaoxing 312000, China

Mathematics, 2024, vol. 12, issue 17, 1-21

Abstract: In this work, quasi-periodic and periodic vibration responses of an axially moving beam are analytically investigated under multiple-frequency excitation. The governing equation is transformed into a nonlinear differential equation by applying the Galerkin method. A double multiple-scales method is used to study the quasi-periodic and periodic vibrations of an axially moving beam with varying velocity and external excitation. Time traces and phase-plane portraits of quasi-periodic and periodic vibrations are obtained, which are in excellent agreement with those of the direct time integration method. The response frequencies of the axially moving beam are determined through the fast Fourier transform (FFT) method. The frequency–amplitude responses of the beam are analytically obtained and its stability is also determined. Lastly, the effects of system parameters on the quasi-periodic and periodic vibration are analyzed.

Keywords: quasi-periodic vibration; multiple-frequency excitation; multiple-scales method; frequency–amplitude response (search for similar items in EconPapers)
JEL-codes: C (search for similar items in EconPapers)
Date: 2024
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