Skip to main content
SpringerLink
Log in

Wave Finite Element Schemes for Vibrations and Noise Under Turbulent Boundary Layer Excitation

  • Conference paper
  • First Online:
Flinovia—Flow Induced Noise and Vibration Issues and Aspects-III (FLINOVIA 2019)

  • 505 Accesses

Abstract

In the framework of finite elements based methods, this work proposes two numerical approaches to deal with the vibrations and noise induced by a random excitation on periodic and homogeneous structural systems. First, a 1D Wave Finite Element scheme is developed to deal with flat, curved and tapered finite structures. A single substructure is modelled using finite elements and one-dimensional periodic links among nodes are applied to get the set of waves propagating along the periodicity direction. The set of waves is then used to calculate the Green transfer functions between a set of target degrees of freedom and a subset representing the loaded ones. A 2D approach is also developed in combination with a wavenumber-space load synthesis to simulate the sound transmission of infinite flat, curved and axisymmetric structures: both homogenised and complex periodic models are analysed. The proposed numerical approaches are validated with analytical, numerical and experimental results and under different load conditions. From the experimental point of view, the approach is validated comparing results in terms of transmission loss evaluated on aircraft fuselage panels under diffuse acoustic field excitation.

This is a preview of subscription content, log in via an institution to check access.

Access this chapter

Log in via an institution
Chapter
USD 29.95
Price excludes VAT (USA)
  • Available as PDF
  • Read on any device
  • Instant download
  • Own it forever
eBook
USD 219.00
Price excludes VAT (USA)
  • Available as EPUB and PDF
  • Read on any device
  • Instant download
  • Own it forever
Softcover Book
USD 279.99
Price excludes VAT (USA)
  • Compact, lightweight edition
  • Dispatched in 3 to 5 business days
  • Free shipping worldwide - see info
Hardcover Book
USD 279.99
Price excludes VAT (USA)
  • Durable hardcover edition
  • Dispatched in 3 to 5 business days
  • Free shipping worldwide - see info

Tax calculation will be finalised at checkout

Purchases are for personal use only

Institutional subscriptions

References

  1. J. Allard, N. Atalla, Propagation of sound in porous media: modelling sound absorbing materials. Wiley (2009). https://doi.org/10.1002/9780470747339

  2. W. Bhat, Flight test measurement of measurement of exterior turbulent boundary layer pressure fluctuations on boeing model 737 airplane. J. Sound Vib. 14(4), 439–457 (1971)

    Google Scholar 

  3. F. Birgersson, N. Ferguson, S. Finnveden, Application of the spectral finite element method to turbulent boundary layer induced vibration of plates. J. Sound Vib. 259(4), 873–891 (2003). https://doi.org/10.1006/jsvi.2002.5127, http://www.sciencedirect.com/science/article/pii/S0022460X02951278

  4. D.E. Bishop, Cruise flight noise levels in a turbojet transport airplane. Noise Control 7(2), 37–42 (1961). https://doi.org/10.1121/1.2369437

  5. F. Bloch, Über die quantenmechanik der elektronen in kristallgittern. Zeitschrift für Physik 52(7), 555–600 (1929). https://doi.org/10.1007/BF01339455

  6. W.K. Bonness, J.B. Fahnline, P.D. Lysak, M.R. Shepherd, Modal forcing functions for structural vibration from turbulent boundary layer flow. J. Sound Vib. 395, 224–239 (2017). https://doi.org/10.1016/j.jsv.2017.02.023, http://www.sciencedirect.com/science/article/pii/S0022460X17301177

  7. D. Chase, Modelling the wavevector-frequency spectrum of turbulent boundary layer wall pressure. J. Sound Vib. 70(1), 29–67 (1953). https://doi.org/10.1016/0022-460X(80)90553-2

  8. E. Ciappi, F. Magionesi, S.D. Rosa, F. Franco, Analysis of the scaling laws for the turbulence driven panel responses. J. Fluids Struct. 32, 90–103 (2012). https://doi.org/10.1016/j.jfluidstructs.2011.11.003

  9. J. Cockburn, J. Robertson, Vibration response of spacecraft shrouds to in-flight fluctuating pressures. J. Sound Vib. 33(4), 399–425 (1974). https://doi.org/10.1016/S0022-460X(74)80226-9

  10. G. Corcos, Resolution of pressure in turbulence. J. Acoust. Soc. Am. 35, 192–199 (1963). https://doi.org/10.1121/1.1918431

  11. V. D’Alessandro, Investigation and assessment of the wave and finite element method for structural waveguides. PhD thesis, University of Naples Federico II (2014). http://www.fedoa.unina.it/9931/

  12. S. De Rosa, F. Franco, E. Ciappi, A simplified method for the analysis of the stochastic response in discrete coordinates. J. Sound Vib. 339, 359–375 (2015). https://doi.org/10.1016/j.jsv.2014.11.010

  13. S. De Rosa, F. Franco, Exact and numerical responses of a plate under a turbulent boundary layer excitation. J. Fluids Struct 24, 212–230 (2008). https://doi.org/10.1016/j.jfluidstructs.2007.07.007

  14. S. De Rosa, F. Franco, A scaling procedure for the response of an isolated system with high modal overlap factor. Mech Syst Signal Process 22, 1549–1565 (2008). https://doi.org/10.1016/j.ymssp.2008.01.007

  15. S. De Rosa, F. Franco, D. Gaudino, Numerical investigations on the turbulence driven responses of a plate in the subcritical frequency range. Wind Struct. Int. J. 15(3), 247–261 (2012)

    Article  Google Scholar 

  16. E. Dowell, Aeroelasticity of plates and shells. Mechanics: Dynamical Systems (Springer, Netherlands, 1974). https://books.google.fr/books?id=qRpof4bV-VoC

  17. C. Droz, J.P. Laine, M. Ichchou, G. Inquiete, A reduced formulation for the free-wave propagation analysis in composite structures. Compos. Struct. 113, 134–144 (2014). https://doi.org/10.1016/j.compstruct.2014.03.017

  18. E.H. Dowell, C. Ventres, Flutter of low aspect ratio plates. AIAA J. 8(6), 1162–1164 (1970). https://doi.org/10.2514/3.5858

  19. I. Elishakoff, Probabilistic Method in Theory of Structures (Wiley, New York, 1983). https://doi.org/10.2514/3.48790

  20. F. Errico, S. De Rosa, F. Franco, G. Petrone, M. Ichchou, Aeroelastic effects on the wave propagation and sound transmission of plates and shells. AIAA J. 58(5) (2019). https://doi.org/10.2514/1.J058722

  21. Errico, F., Ichchou, M., De Rosa, S., Bareille, O., Franco, F.: The modelling of the flow-induced vibrations of periodic flat and axial-symmetric structures with a wave-based method. J. Sound Vib. 424, 32–47 (2018). https://doi.org/10.1016/j.jsv.2018.03.012

  22. F. Errico, M. Ichchou, S. De Rosa, O. Bareille, F. Franco, A WFE and hybrid FE/WFE technique for the forced response of stiffened cylinders. Adv. Aircr. Spacecr. Sci. Int. J. 5(1), 1–16 (2018). https://doi.org/10.12989/aas.2018.5.1.0012

  23. F. Errico, M. Ichchou, F. Franco, S. De Rosa, O. Bareille, C. Droz, Schemes for the sound transmission of flat, curved and axisymmetric structures excited by aerodynamic and acoustic sources. J. Sound Vib. 476, 221–238 (2019). https://doi.org/10.1016/j.jsv.2019.05.041

  24. F. Errico, G. Tufano, O. Robin, N. Guenfoud, M. Ichchou, N. Atalla, Simulating the sound transmission loss of complex curved panels with attached noise control materials using periodic cell wavemodes. Appl. Acoust. 156, 21–28 (2019). https://doi.org/10.1016/j.apacoust.2019.06.027, http://www.sciencedirect.com/science/article/pii/S0003682X1930177X

  25. S. Finnveden, Evaluation of modal density and group velocity by a finite element method. J. Sound Vib. 273(1), 51–75 (2004). https://doi.org/10.1016/j.jsv.2003.04.004, http://www.sciencedirect.com/science/article/pii/S0022460X03008897

  26. S. Finnveden, F. Birgersson, U. Ross, T. Kremer, A model of wall pressure correlation for prediction of turbulence-induced vibration. J. Fluids Struct. 20(8), 1127–1143 (2005). https://doi.org/10.1016/j.jfluidstructs.2005.05.012, http://www.sciencedirect.com/science/article/pii/S0889974605000885

  27. F. Franco, S. De Rosa, E. Ciappi, Numerical approximations on the predictive responses of plates under stochastic and convective loads. J. Fluids Struct. 42, 296–312 (2013). https://doi.org/10.1016/j.jfluidstructs.2013.06.006

  28. S. Ghinet, N. Atalla, H. Osman, Diffuse field transmission into infinite sandwich composite and laminate composite cylinders. J. Sound Vib. 289, 745–778 (2006). https://doi.org/10.1016/j.jsv.2005.02.028

  29. W. Graham, A comparison of models for the wavenumber-frequency spectrum of turbolent boundary layer pressures. J. Sound Vib. 206(4), 541–565 (1997). https://doi.org/10.1006/jsvi.1997.1114

  30. S. Hambric, Y. Hwang, W. Bonness, Vibrations of plates with clamped and free edges excited by low-speed turbulent boundary layer flow. J. Fluids Struct. 19(1), 93–110 (2004). https://doi.org/10.1016/j.jfluidstructs.2003.09.002

  31. M. Ichchou, O. Bareille, Y. Jacques, Energy predictions of turbulent boundary layer induced mid-high frequency structural vibrations. J.. Wind Eng. Ind. Aerodyn. 97(2), 63–76 (2009). https://doi.org/10.1016/j.jweia.2008.11.001, http://www.sciencedirect.com/science/article/pii/S0167610508001761

  32. M. Ichchou, B. Hiverniau, B. Troclet, Equivalent rain on the roof loads for random spatially correlated excitations in the mid frequency range. J. Sound Vib. 322, 926–940 (2009). https://doi.org/10.1016/j.jsv.2008.11.050

  33. F. Leppington, E. Broadbent, K. Heron, The acoustic radiation efficiency from rectangular plates. Proc. R. Soc. 382, 245–271 (1982). https://doi.org/10.1098/rspa.1982.0100

  34. Y. Li, Y. Zhang, D. Kennedy, Random vibration analysis of axially compressed cylindrical shells under turbulent boundary layer in a symplectic system. J. Sound Vib. 406, 161–180 (2017). https://doi.org/10.1016/j.jsv.2017.06.018

  35. E. Manconi, B.R. Mace, Modelling wave propagation in two dimensional structures using finite element analysis. J. Sound Vib. 318(45)

    Google Scholar 

  36. L. Maxit, Simulation of the pressure field beneath a turbulent boundary layer using realisations of uncorrelated wall plane waves. J. Acoust. Soc. Am. 140, 1268–1285 (2016)

    Article  Google Scholar 

  37. J.M. Mencik, On the low- and mid-frequency forced response of elastic structures using wave finite elements with one-dimensional propagation. Comput. Struct. 88, 674–689 (2010). https://doi.org/10.1016/j.compstruc.2010.02.006

  38. J.M. Mencik, M. Ichchou, Wave finite elements in guided elastodynamics with internal fluid. Int. J. Solids Struct. 44(7.8), 2148–2167 (2007). https://doi.org/10.1016/j.ijsolstr.2006.06.048

  39. J. Miles, On the aerodynamic instability of thin panels. J. Aeronaut. Sci. 23(8), 771–791 (1956)

    Article  MathSciNet  Google Scholar 

  40. G. Mitrou, N. Ferguson, J. Renno, Wave transmission through two-dimensional structures by the hybrid fe/wfe approach. J. Sound Vib. 389, 484–501 (2017). https://doi.org/10.1016/j.jsv.2016.09.032, http://www.sciencedirect.com/science/article/pii/S0022460X16305004

  41. U. Orrenius, V. Cotoni, A. Wareing, Analysis of sound transmission through aircraft fuselages excited by turbulent boundary layer or diffuse acoustic pressure fields, in 38th International Congress and Exposition on Noise Control Engineering 2009, INTER-NOISE 2009, vol. 4 (2009), pp. 2637–2645

    Google Scholar 

  42. U. Orrenius, H. Liu, A. Wareing, S. Finnveden, V. Cotoni, Wave modelling in predictive vibro-acoustics: applications to rail vehicles and aircraft. Wave Motion 51(4), 635–649 (2014). https://doi.org/10.1016/j.wavemoti.2013.11.007

  43. J. Renno, B. Mace, Calculating the forced response of cylinders using the wave and finite element method. J. Sound Vib. 333, 5340–5355 (2014). https://doi.org/10.1016/j.jsv.2014.04.042

  44. J.M. Renno, B.R Mace, Vibration modelling of structural networks using a hybrid finite element/wave and finite element approach. Wave Motion 51(4), 566–580 (2014). https://doi.org/10.1016/j.wavemoti.2013.09.001

  45. D. Rhazi, N. Atalla, A simple method to account for finite size effects in the transfer matrix method. J. Acoust. Soc. Am. 127(2), EL30–EL36 (2010). https://doi.org/10.1121/1.3280237

  46. J. Rocha, Impact of the chosen turbulent flow empirical model on the prediction of sound radiation and vibration by aircraft panels. J. Sound Vib. 373, 285–301 (2016). https://doi.org/10.1016/j.jsv.2016.03.026, http://www.sciencedirect.com/science/article/pii/S0022460X16300013

  47. J.L.T. da Rocha, Coupled structural-acoustic analytical models for the prediction of turbulent boundary-layer-induced noise in aircraft cabins. PhD thesis, University of Victoria (2010)

    Google Scholar 

  48. W. Rodden, E. Farkas, H. Malcom, A. Kliszewski, Aerodynamic influence coefficients from supersonic strip theory: analytical development and computational procedure. Defense Technical Information Center (1962). https://books.google.fr/books?id=pBi5twAACAAJ

  49. A. Smol’yakov, V. Tkachenko, Model of pseudosonic turbulent wall pressures and experimental data. Sov. Phys. Acoust. 37(6), 627–631 (1991). https://doi.org/10.1121/1.4960516

  50. G. Tufano, F. Errico, O. Robin, C. Droz, M. Ichchou, B. Pluymers, W. Desmet, N. Atalla, K-space analysis of complex large-scale meta-structures using the inhomogeneous wave correlation method. Mech. Syst. Signal Process. 135, 106407 (2020). https://doi.org/10.1016/j.ymssp.2019.106407, http://www.sciencedirect.com/science/article/pii/S0888327019306284

  51. M. Villot, C. Guigou, L. Gagliardini, Predicting the acoustical radiation of finite size multi-layered structures by applying spatial windowing on infinite structures. J. Sound Vib. 245(3), 433–455 (2001). https://doi.org/10.1006/jsvi.2001.3592

  52. Y. Waki, B. Mace, B., Brennan, M, Numerical issues concerning the wave and finite element method for free and forced vibrations of waveguides. J. Sound Vib. 327, 92–108 (2009)

    Google Scholar 

  53. K. Waye, On the effects on environmental low frequency noise. Technical report, Department of Environmental Medicine, Goteborg University Publication (1995)

    Google Scholar 

  54. C. Zhou, J.P. Laine, M. Ichchou, A. Zine, Wave finite element method based on reduced model for one-dimensional periodic structures. Int. J. Appl. Mech. 7(2), 32–47 (2015). https://doi.org/10.1142/S1758825115500180

Download references

Acknowledgements

This project has received funding from the European Union Horizon 2020 research and innovation programme under the Marie Sklodowska-Curie grant agreement No. 675441.

Author information

Authors and Affiliations

  1. Ecole Centrale de Lyon, 36 Avenue Guy de Collongue, Lyon, France

    Fabrizio Errico & Mohamed Ichchou

  2. Universitá di Napoli Federico II, Via Claudio 21, Napoli, Italy

    Francesco Franco, Sergio De Rosa & Giuseppe Petrone

Authors
  1. Fabrizio Errico
    View author publications

    You can also search for this author in PubMed Google Scholar

  2. Francesco Franco
    View author publications

    You can also search for this author in PubMed Google Scholar

  3. Sergio De Rosa
    View author publications

    You can also search for this author in PubMed Google Scholar

  4. Giuseppe Petrone
    View author publications

    You can also search for this author in PubMed Google Scholar

  5. Mohamed Ichchou
    View author publications

    You can also search for this author in PubMed Google Scholar

Corresponding author

Correspondence to Fabrizio Errico .

Editor information

Editors and Affiliations

  1. CNR-INSEAN, Rome, Italy

    Elena Ciappi

  2. DII, University of Naples Federico II, Napoli, Italy

    Sergio De Rosa

  3. DII, University of Naples Federico II, Napoli, Italy

    Francesco Franco

  4. ARL, Pennsylvania State University, State College, PA, USA

    Stephen A. Hambric

  5. Dept of Mechanical Engineering, Hong Kong Polytechnic University, Hung Hom, Kowloon, Hong Kong

    Randolph C. K. Leung

  6. École Centrale de Lyon, Écully, France

    Vincent Clair

  7. Laboratoire Vibrations Acoustique, University of Lyon, INSA-Lyon, Villeurbanne, France

    Laurent Maxit

  8. Laboratoire Vibrations Acoustique, University of Lyon, INSA-Lyon, Villeurbanne, France

    Nicolas Totaro

Rights and permissions

Reprints and permissions

Copyright information

© 2021 The Author(s), under exclusive license to Springer Nature Switzerland AG

About this paper

Check for updates. Verify currency and authenticity via CrossMark

Cite this paper

Errico, F., Franco, F., De Rosa, S., Petrone, G., Ichchou, M. (2021). Wave Finite Element Schemes for Vibrations and Noise Under Turbulent Boundary Layer Excitation. In: Ciappi, E., et al. Flinovia—Flow Induced Noise and Vibration Issues and Aspects-III. FLINOVIA 2019. Springer, Cham. https://doi.org/10.1007/978-3-030-64807-7_15

Download citation

  • DOI: https://doi.org/10.1007/978-3-030-64807-7_15

  • Published:

  • Publisher Name: Springer, Cham

  • Print ISBN: 978-3-030-64806-0

  • Online ISBN: 978-3-030-64807-7

  • eBook Packages: EngineeringEngineering (R0)

Publish with us

Policies and ethics

Search

Navigation