Steady-State Periodic Responses of a Viscoelastic Buckled Beam in Nonlinear Internal Resonance

XIONG Liu-yang; ZHANG Guo-ce; DING Hu; CHEN Li-qun

doi:10.3879/j.issn.1000-0887.2014.11.002

Volume 35 Issue 11

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XIONG Liu-yang, ZHANG Guo-ce, DING Hu, CHEN Li-qun. Steady-State Periodic Responses of a Viscoelastic Buckled Beam in Nonlinear Internal Resonance[J]. Applied Mathematics and Mechanics, 2014, 35(11): 1188-1196. doi: 10.3879/j.issn.1000-0887.2014.11.002

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Steady-State Periodic Responses of a Viscoelastic Buckled Beam in Nonlinear Internal Resonance

doi: 10.3879/j.issn.1000-0887.2014.11.002

¹Shanghai Institute of Applied Mathematics and Mechanics, Shanghai University, Shanghai 200072, P.R.China;²Department of Mechanics, Shanghai University, Shanghai 200444, P.R.China;³Shanghai Key Laboratory of Mechanics in Energy Engineering, Shanghai 200072, P.R.China

Funds: The National Natural Science Foundation of China(Key Program)(11232009); The National Natural Science Foundation of China(11372171;11422214)

Received Date: 2014-05-23
Publish Date: 2014-11-18

Abstract

Abstract

Nonlinear vibration of a hinged-hinged viscoelastic buckled beam subjected to primary resonance in the presence of internal resonance was investigated. The governing integro-partial differential equation was derived via introduction of coordinate transform for the non-trivial equilibrium configuration, with the viscoelastic constitutive relation taken into account. Based on the Galerkin method, the governing equation was truncated to a set of infinite ordinary differential equations and the condition for internal resonance was obtained. The multiple scales method was applied to derive the modulation-phase equations. Steady-state periodic solutions to the system as well as their stability were determined. The numerical examples were focused on the nonlinear phenomena, such as double-jump and hysteresis. The generation and vanishing of a double-jumping phenomenon on the amplitude-frequency curves were discussed in detail. The Runge-Kutta method was developed to verify the accuracy of results from the multiple scales method.
- buckled beam,
- viscoelasticity,
- internal resonance,
- multiple scales method,
- stability

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References(12)

References

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