Parametric resonance of axially moving Timoshenko beams with time-dependent speed

You Qi Tang; Li Qun Chen; Xiao Dong Yang

doi:10.1007/s11071-009-9512-1

Parametric resonance of axially moving Timoshenko beams with time-dependent speed

You Qi Tang
, Li Qun Chen^*
, Xiao Dong Yang

^*Corresponding author for this work

Shanghai University
Shenyang Aerospace University

Research output: Contribution to journal › Article › peer-review

52 Scopus citations

Abstract

In this paper, parametric resonance of axially moving beams with time-dependent speed is analyzed, based on the Timoshenko model. The Hamilton principle is employed to obtain the governing equation, which is a nonlinear partial-differential equation due to the geometric nonlinearity caused by the finite stretch of the beam. The method of multiple scales is applied to predict the steady-state response. The expression of the amplitude of the steady-state response is derived from the solvability condition of eliminating secular terms. The stability of straight equilibrium and nontrivial steady-state response are analyzed by using the Lyapunov linearized stability theory. Some numerical examples are presented to demonstrate the effects of speed pulsation and the nonlinearity in the first two principal parametric resonances.

Original language	English
Pages (from-to)	715-724
Number of pages	10
Journal	Nonlinear Dynamics
Volume	58
Issue number	4
DOIs	https://doi.org/10.1007/s11071-009-9512-1
State	Published - Dec 2009
Externally published	Yes

Keywords

Axially moving Timoshenko beams
Method of multiple scales
Parametric resonance
Steady-state response

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10.1007/s11071-009-9512-1

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abstract = "In this paper, parametric resonance of axially moving beams with time-dependent speed is analyzed, based on the Timoshenko model. The Hamilton principle is employed to obtain the governing equation, which is a nonlinear partial-differential equation due to the geometric nonlinearity caused by the finite stretch of the beam. The method of multiple scales is applied to predict the steady-state response. The expression of the amplitude of the steady-state response is derived from the solvability condition of eliminating secular terms. The stability of straight equilibrium and nontrivial steady-state response are analyzed by using the Lyapunov linearized stability theory. Some numerical examples are presented to demonstrate the effects of speed pulsation and the nonlinearity in the first two principal parametric resonances.",

keywords = "Axially moving Timoshenko beams, Method of multiple scales, Parametric resonance, Steady-state response",

author = "Tang, \{You Qi\} and Chen, \{Li Qun\} and Yang, \{Xiao Dong\}",

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T1 - Parametric resonance of axially moving Timoshenko beams with time-dependent speed

AU - Tang, You Qi

AU - Chen, Li Qun

AU - Yang, Xiao Dong

PY - 2009/12

Y1 - 2009/12

N2 - In this paper, parametric resonance of axially moving beams with time-dependent speed is analyzed, based on the Timoshenko model. The Hamilton principle is employed to obtain the governing equation, which is a nonlinear partial-differential equation due to the geometric nonlinearity caused by the finite stretch of the beam. The method of multiple scales is applied to predict the steady-state response. The expression of the amplitude of the steady-state response is derived from the solvability condition of eliminating secular terms. The stability of straight equilibrium and nontrivial steady-state response are analyzed by using the Lyapunov linearized stability theory. Some numerical examples are presented to demonstrate the effects of speed pulsation and the nonlinearity in the first two principal parametric resonances.

AB - In this paper, parametric resonance of axially moving beams with time-dependent speed is analyzed, based on the Timoshenko model. The Hamilton principle is employed to obtain the governing equation, which is a nonlinear partial-differential equation due to the geometric nonlinearity caused by the finite stretch of the beam. The method of multiple scales is applied to predict the steady-state response. The expression of the amplitude of the steady-state response is derived from the solvability condition of eliminating secular terms. The stability of straight equilibrium and nontrivial steady-state response are analyzed by using the Lyapunov linearized stability theory. Some numerical examples are presented to demonstrate the effects of speed pulsation and the nonlinearity in the first two principal parametric resonances.

KW - Axially moving Timoshenko beams

KW - Method of multiple scales

KW - Parametric resonance

KW - Steady-state response

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DO - 10.1007/s11071-009-9512-1

M3 - 文章

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SN - 0924-090X

VL - 58

SP - 715

EP - 724

JO - Nonlinear Dynamics

JF - Nonlinear Dynamics

IS - 4

ER -

Parametric resonance of axially moving Timoshenko beams with time-dependent speed

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Keywords

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