Bifurcations and chaotic motions in the autonomous system of a restrained pipe conveying fluid

Jiang, Jiwang; Zou, Guoping

doi:10.1016/s0022-460x(02)00982-3

Cited by 37 publications

(21 citation statements)

References 12 publications

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“…Case A: when λ 2 is fixed and λ 1 is changed, α can be denoted as a function of λ 2 from Eq. (8). Thus the hysteresis set H 1 satisfies…”

Section: Hysteresis Setmentioning

confidence: 96%

“…In 1996, Bi and Chen [7] studied the universal unfolding of a nonlinear vibration mill and obtained all kinds of dynamical phenomena of the system. In 2003, Jin and Zou [8] applied singularity theory to a restrained pipe conveying fluid and obtained the dynamical behavior in different persistent regions. In the last few years, the singularity theory has been employed to study the dynamic behavior in rotary machine [9,10].…”

Section: Introductionmentioning

confidence: 99%

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Singular analysis of bifurcation systems with two parameters

Qin

Chen

2010

Acta Mech Sin

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Bifurcation properties of dynamical systems with two parameters are investigated in this paper. The definition of transition set is proposed, and the approach developed is used to investigate the dynamic characteristic of the nonlinear forced Duffing system with nonlinear feedback controller. The whole parametric plane is divided into several persistent regions by the transition set, and then the bifurcation diagrams in different persistent regions are obtained.

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“…Case A: when λ 2 is fixed and λ 1 is changed, α can be denoted as a function of λ 2 from Eq. (8). Thus the hysteresis set H 1 satisfies…”

Section: Hysteresis Setmentioning

confidence: 96%

Section: Introductionmentioning

confidence: 99%

Singular analysis of bifurcation systems with two parameters

Qin

Chen

2010

Acta Mech Sin

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“…When ω 2 = 1, and Ω 2 = 2 + εσ 2 , for (19), the parameter excited resonance will occur according to Ref. [28].…”

Section: Stability and Local Bifurcation Analysis For Positive Stiffnmentioning

confidence: 98%

Section: Stability and Local Bifurcation Analysis Of Parametric Excitmentioning

confidence: 99%

“…The coefficients in (19) and (20) are shown in Appendix A. Since the positive stiffness and the negative stiffness introduce different nonlinearities, as shown in (19) and (20), they have to be analyzed separately. The analysis procedure and the results for the case of the positive stiffness are discussed in detail, while only the necessary results for the case of negative stiffness are presented due to the similarity of the two analysis procedures.…”

Section: Stability and Local Bifurcation Analysis Of Parametric Excitmentioning

confidence: 99%

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Stability and local bifurcation of parameter-excited vibration of pipes conveying pulsating fluid under thermal loading

Zhao

Liu

2015

Appl. Math. Mech.-Engl. Ed.

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The parametric excited vibration of a pipe under thermal loading may occur because the fluid is often transported heatedly. The effects of thermal loading on the pipe stability and local bifurcations have rarely been studied. The stability and the local bifurcations of the lateral parametric resonance of the pipe induced by the pulsating fluid velocity and the thermal loading are studied. A mathematical model for a simply supported pipe is developed according to the Hamilton principle. Two partial differential equations describing the lateral and longitudinal vibration are obtained. The singularity theory is utilized to analyze the stability and the bifurcation of the system solutions. The transition sets and the bifurcation diagrams are obtained both in the unfolding parameter space and the physical parameter space, which can reveal the relationship between the thermal field parameter and the dynamic behaviors of the pipe. The frequency response and the relationship between the critical thermal rate and the pulsating fluid velocity are obtained. The numerical results demonstrate the accuracy of the single-mode expansion of the solution and the stability and local bifurcation analyses. It also confirms the existence of the chaos. The presented work can provide valuable information for the design of the pipeline and the controllers to prevent the structural instability.

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References

2017

Handbook of Structural Life Assessment

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Bifurcations and chaotic motions in the autonomous system of a restrained pipe conveying fluid

Cited by 37 publications

References 12 publications

Singular analysis of bifurcation systems with two parameters

Singular analysis of bifurcation systems with two parameters

Stability and local bifurcation of parameter-excited vibration of pipes conveying pulsating fluid under thermal loading

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