Internal resonance of pipes conveying fluid in the supercritical regime

Zhang, Yanlei; Chen, Liqun

doi:10.1007/s11071-011-0084-5

Cited by 54 publications

(10 citation statements)

References 13 publications

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“…Zhai et al (2011) determined the natural frequencies of fluid-conveying Timoshenko pipes via the complex modal analysis, and calculated the dynamic response of pipeline under random excitation by the pseudo excitation algorithm. Zhang and Chen (2012) analyzed the internal resonance of pipes conveying fluid in the supercritical regime, in which the straight pipe equilibrium configuration becomes unstable and bifurcates into two possible curved equilibrium configurations. As the extension of the previous work, Zhang and Chen (2013) and Chen et al (2014) studied the nonlinear forced vibration of a viscoelastic pipe conveying fluid around the curved equilibrium configuration resulting from the supercritical flow speed, where the frequency and amplitude relationships of stead-state responses in external and internal resonances were derived.…”

Section: Introductionmentioning

confidence: 99%

Dynamic behavior of pipes conveying gas–liquid two-phase flow

2015

Nuclear Engineering and Design

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Section: Introductionmentioning

confidence: 99%

Dynamic behavior of pipes conveying gas–liquid two-phase flow

2015

Nuclear Engineering and Design

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“…Nayfeh [16] pointed that the solvability condition in the method of multiple scales may cast into different forms, and it can be mathematically proved that the different forms are equivalent only in the two-degree-of-freedom systems. Recently, Chen and Zhang [17] developed a general framework of multiple scales analysis on the nonlinear gyroscopic system for the first time, and they observed that the different forms of the solvability condition for a four-degree-of-freedom system are equivalent when studied the forced vibration of pipes conveying fluid [18,19]. In the present paper, Chen and Zhang's general framework is developed to analysis a higher degree-of-freedom vibration system.…”

Section: Introductionmentioning

confidence: 91%

Nonlinear vibration of rotating pre-deformed blade with thermal gradient

Zhang

2016

Nonlinear Dyn

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In this paper, the nonlinear dynamic behavior is investigated for a rotating pre-deformed pretwisted blade subjected to harmonic gas pressure. The pre-deformation curve produced by thermal gradient is derived. A novel nonlinear vibration system is established by considering the influence of pre-deformation. The combination of the Lagrange principle and the assumed modes method is utilized to obtain the motion equations, and then the equations are transformed into a dimensionless form through introducing a set of dimensionless parameters. For the purpose of ensuring high precision in determination of the internal resonance condition, the equations of motion are discretized by adequate trial functions. An eigenvalue analysis is conducted on the corresponding linear system to obtain the natural frequencies and examine the possibility of the 2:1 internal resonance. The method of multiple scales is developed to solve the resulting multi-degree-offreedom nonlinear ordinary differential equations. A numerical integration by means of Runge-Kutta is performed to establish the validity of the derived formulations. The evolution of frequency response curves with the rotating speed is observed. The influences of the thermal gradient, gas pressure and damping coefficient on the resonant dynamics of the system are investigated in detail. For the purpose of comparison, another distribution profile of pre-deformation, which is frequently used in previous literature, is also examined. It could be found that not only the amplitude but also the distribution of the initial deflection could influence the steadystate nonlinear response of the pre-deformed blade. A series of interesting nonlinear dynamic phenomena are discovered from the results.

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“…Yamashita et al [5] used theoretically analysis and experimental verification to study the selfexcited nonplanar motion of the vertical cantilevered pipe subjected the horizontal external excitation. Zhang et al [6,7] studied the internal resonance and external resonance of pipe conveying fluid in the supercritical flow speed through the analytical results and the numerical integrations.…”

Section: Introductionmentioning

confidence: 99%

Natural Characteristic of Thin-Wall Pipe under Uniformly Distributed Pressure

Tang

She

et al. 2018

Chin. J. Mech. Eng.

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Natural characteristics of thin-wall pipe of the compressor under uniformly distributed pressure were presented in this paper based on a cylindrical shell model. In the traditional method, the beam model was usually used to analyze the pipe system. In actual fact, the pipe segment of the compressor was always broken in the form of a long crack or a partial hole and the phenomenon was hardly explained by beam model. According to the structure characteristic of compressor pipe segment, whose radius is large and thickness is little, shell model shows the advantage in this kind of pipe problem. Based on Sanders' shell theory, the vibration differential equation of pipe was established by applying the energy method. The influences of length to radius ratio (L/R), thickness to radius ratio (h/R), circumferential wave number (n) and pressure (q) on the natural frequencies of pipe were analyzed. The study shows: Pressure and structural parameters have a great effect on the natural characteristics of the pipe. Natural frequency increases as the pressure increases, especially for the higher mode. The sensitivity of natural frequency on pressure becomes stronger with h/R ratio increases; when L/R ratio is greater than a certain critical value, the influence of the pressure on natural frequency will no longer be obvious. The value of n corresponding to the minimum natural frequency also depends on the value of pressure. In the end, analysis of the forced vibration of a specific pipeline model was given and the modal shapes were illustrated to understand the break of the pipe. The research here will provide the theory support for the dynamic design of related pressure pipe and further experiment study should be employed.

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Internal resonance of pipes conveying fluid in the supercritical regime

Cited by 54 publications

References 13 publications

Dynamic behavior of pipes conveying gas–liquid two-phase flow

Dynamic behavior of pipes conveying gas–liquid two-phase flow

Nonlinear vibration of rotating pre-deformed blade with thermal gradient

Natural Characteristic of Thin-Wall Pipe under Uniformly Distributed Pressure

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