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Technical Brief

Forced Response Analysis of Pipes Conveying Fluid by Nonlinear Normal Modes Method and Iterative Approach

[+] Author and Article Information
Feng Liang

School of Energy and Power Engineering,
Shenyang University of Chemical Technology,
Shenyang 110142, China;
College of Mechanical Engineering and
Applied Electronics,
Beijing University of Technology,
Beijing 100124, China
e-mail: lf84411@163.com

Xiao-Dong Yang

College of Mechanical Engineering and
Applied Electronics,
Beijing University of Technology,
Beijing 100124, China
e-mail: jxdyang@163.com

Ying-Jing Qian

College of Mechanical Engineering and
Applied Electronics,
Beijing University of Technology,
Beijing 100124, China
e-mail: candiceqyj@163.com

Wei Zhang

College of Mechanical Engineering and
Applied Electronics,
Beijing University of Technology,
Beijing 100124, China
e-mail: sandyzhang0@yahoo.com

1Corresponding author.

Contributed by the Design Engineering Division of ASME for publication in the JOURNAL OF COMPUTATIONAL AND NONLINEAR DYNAMICS. Manuscript received December 18, 2016; final manuscript received August 2, 2017; published online October 9, 2017. Assoc. Editor: Katrin Ellermann.

J. Comput. Nonlinear Dynam 13(1), 014502 (Oct 09, 2017) (5 pages) Paper No: CND-16-1627; doi: 10.1115/1.4037594 History: Received December 18, 2016; Revised August 02, 2017

The forced vibration of gyroscopic continua is investigated by taking the pipes conveying fluid as an example. The nonlinear normal modes and a numerical iterative approach are used to perform numerical response analysis. The nonlinear nonautonomous governing equations are transformed into a set of pseudo-autonomous ones by using the harmonic balance method. Based on the pseudo-autonomous system, the nonlinear normal modes are constructed by the invariant manifold method on the state space and substituted back into the original discrete equations. By repeating the above mentioned steps, the dynamic responses can be numerically obtained asymptotically using such iterative approach. Quadrature phase difference between the general coordinates is verified for the gyroscopic system and traveling waves instead of standing waves are found in the time-domain complex modal analysis.

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Figures

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Fig. 1

Mechanical model of a forced pipe conveying fluid

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Fig. 2

The frequency–amplitude responses of the pipes conveying fluid: (a) the first general coordinate q1 and (b) the second general coordinate q2

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Fig. 3

The time histories of q1, p1, q2, and p2 during forced vibrations

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Fig. 4

The snapshots during modal motions: (a) a pipe conveying fluid (gyroscopic system) and (b) a pipe without moving fluid (nongyroscopic system)

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