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Analysis of linear elastic wave propagation in piping systems by a combination of the boundary integral equations method and the finite element method

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Abstract

The combined methodology of boundary integral equations and finite elements is formulated and applied to study the wave propagation phenomena in compound piping systems consisting of straight and curved pipe segments with compact elastic supports. This methodology replicates the concept of hierarchical boundary integral equations method proposed by L. I. Slepyan to model the time-harmonic wave propagation in wave guides, which have components of different dimensions. However, the formulation presented in this article is tuned to match the finite element format, and therefore, it employs the dynamical stiffness matrix to describe wave guide properties of all components of the assembled structure. This matrix may readily be derived from the boundary integral equations, and such a derivation is superior over the conventional derivation from the transfer matrix. The proposed methodology is verified in several examples and applied for analysis of periodicity effects in compound piping systems of several alternative layouts.

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Abbreviations

FE:

Finite element

BIE:

Boundary integral equations

References

  1. Slepyan L.I., Sorokin S.V.: Boundary integral equations of interaction between thin-walled structures and continuous media (in Russian). Proc. Acad. Sci. USSR 306, 1332–1335 (1989)

    MathSciNet  Google Scholar 

  2. Slepyan L.I., Sorokin S.V.: The boundary integral equations method in hydroelasticity (in Russian). Izv. Akad. Nauk SSSR [Mech. Rigid Body] 4, 166–176 (1989)

    Google Scholar 

  3. Slepyan L.I., Sorokin S.V.: A system of boundary integral equations for dynamics of complex thin-walled structures in contact with an acoustic medium (in Russian). Izv. Akad. Nauk SSSR [Mech. Rigid Body] 4, 113–121 (1990)

    Google Scholar 

  4. Slepyan L.I., Sorokin S.V.: Analysis of structural-acoustic coupling problems by a two-level boundary integral equations method. Part 1. A general formulation and test problems. J. Sound Vib. 184(2), 195–212 (1995)

    Article  MATH  ADS  Google Scholar 

  5. Søe-Knudsen A.: Modelling of a 3D pipe system containing both straight and curved segments using boundary integral equations method. In: Kvamsdal, T., Mathisen, K.M., Pettersen, B. (eds) Proceedings of the 21st Nordic Seminar on Computational Mechanics, pp. 289–292. Trondheim, Norway (2008)

    Google Scholar 

  6. Søe-Knudsen, A.: Modeling of spatial fluid filled pipe system containing both straight and curved segments using boundary integral equations. In: Papadrakis, M., Lagaros, N.D., Fragiadakis, M. (eds.) Proceedings of the 2nd International Conference on Computational Methods in Structural Dynamics and Earthquake Engineering, Rhodes Island, Greek (2009)

  7. Gopalakrishnan S., Doyle J.F.: Spectral super-elements for wave propagation in structures with local non-uniformities. Comput. Methods Appl. Mech. Eng. 121, 77–90 (1995)

    Article  MATH  ADS  Google Scholar 

  8. Doyle J.F.: Wave Propagation in Structures: Spectral Analysis Using Fast Discrete Fourier Transforms, 2nd ed. Springer-Verlag, New York (1997)

    MATH  Google Scholar 

  9. Shone, S.P.: A flexural wave scattering method for damage detection in beams. Ph.D. thesis, University of Southampton (2006)

  10. Miller D.W., von Flotow A.: A travelling wave approach to power flow in structural networks. J. Sound Vib. 128, 145–162 (1989)

    Article  ADS  Google Scholar 

  11. Floquet M.G.: Sur les equations differentielles linéaires á coefficents périodiques (in French). Annales Scientifiques de L’É.N.S 2, 47–88 (1883)

    MathSciNet  Google Scholar 

  12. Brillouin L.: Wave Propagation in Periodic Structures, 2nd edn. Dover Publications Inc, New York (1953)

    MATH  Google Scholar 

  13. Mead D.J.: Passive Vibration Control. John Wiley & Sons, England (1998)

    Google Scholar 

  14. Rau S.S.: Mechanical Vibrations, 4th ed. Pearson Prentice Hall, New Jersey (2004)

    Google Scholar 

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Authors and Affiliations

  1. Department of Mechanical and Manufacturing Engineering, Aalborg University, Pontoppidanstraede 101, Aalborg East, 9220, Denmark

    A. Søe-Knudsen & S. V. Sorokin

Authors
  1. A. Søe-Knudsen
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  2. S. V. Sorokin
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Correspondence to A. Søe-Knudsen.

Additional information

Communicated by Prof. Peter Smereka.

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Søe-Knudsen, A., Sorokin, S.V. Analysis of linear elastic wave propagation in piping systems by a combination of the boundary integral equations method and the finite element method. Continuum Mech. Thermodyn. 22, 647–662 (2010). https://doi.org/10.1007/s00161-010-0145-x

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  • DOI: https://doi.org/10.1007/s00161-010-0145-x

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