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Steady-state response of a fluid-conveying pipe with 3:1 internal resonance in supercritical regime

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Abstract

The forced vibration response of the pipe conveying fluid, with 3:1 internal resonance, is studied here for the first time. The straight equilibrium configuration becomes bent while the velocity of the fluid exceeds the critical value. As a result, the original mono-stable system transforms to a bi-stable system. Critical excitation which can cause global responses is solved out from the potential equation of the unperturbed system. The condition of 3:1 internal resonance is established after the partial differential equation is discretized. Global bifurcations are studied in simulation ways. By the method of multiple scales, local responses around the bent configuration are investigated. The analytical results are verified by simulations. Responses at the second mode bifurcate out another branch near the resonance frequency. It is very different with the triply harmonic responses without internal resonance. The triply harmonic response is a resonant excitation to the second mode. Responses will change largely with the detuning relationship between these two modes. Influences of the excited amplitude are also studied. Based on the analytical method, critical excited conditions of jumping and hysteretic phenomena are determined. The responses will have up- and down-bifurcations in the special region.

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Acknowledgments

The authors gratefully acknowledge the support of the State Key Program of the National Natural Science Foundation of China (No. 11232009) and the National Natural Science Foundation of China (Nos. 11372171, 11422214).

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Authors and Affiliations

  1. Shanghai Institute of Applied Mathematics and Mechanics, Shanghai University, 149 Yan Chang Road, Shanghai, 200072, China

    Xiao-Ye Mao, Hu Ding & Li-Qun Chen

  2. Shanghai Key Laboratory of Mechanics in Energy Engineering, Shanghai University, Shanghai, 200072, China

    Hu Ding & Li-Qun Chen

  3. Department of Mechanics, Shanghai University, Shanghai, 200444, China

    Li-Qun Chen

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  1. Xiao-Ye Mao
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  2. Hu Ding
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  3. Li-Qun Chen
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Correspondence to Hu Ding.

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Mao, XY., Ding, H. & Chen, LQ. Steady-state response of a fluid-conveying pipe with 3:1 internal resonance in supercritical regime. Nonlinear Dyn 86, 795–809 (2016). https://doi.org/10.1007/s11071-016-2924-9

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  • DOI: https://doi.org/10.1007/s11071-016-2924-9

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