On the use of the wave finite element method for passive vibration control of periodic structures

- Journal title : Advances in aircraft and spacecraft science
- Volume 3, Issue 3, 2016, pp.299-315
- Publisher : Techno-Press
- DOI : 10.12989/aas.2016.3.3.299

Title & Authors

On the use of the wave finite element method for passive vibration control of periodic structures

Silva, Priscilla B.; Mencik, Jean-Mathieu; Arruda, Jose R.F.;

Silva, Priscilla B.; Mencik, Jean-Mathieu; Arruda, Jose R.F.;

Abstract

In this work, a strategy for passive vibration control of periodic structures is proposed which involves adding a periodic array of simple resonant devices for creating band gaps. It is shown that such band gaps can be generated at low frequencies as opposed to the well known Bragg scattering effects when the wavelengths have to meet the length of the elementary cell of a periodic structure. For computational purposes, the wave finite element (WFE) method is investigated, which provides a straightforward and fast numerical means for identifying band gaps through the analysis of dispersion curves. Also, the WFE method constitutes an efficient and fast numerical means for analyzing the impact of band gaps in the attenuation of the frequency response functions of periodic structures. In order to highlight the relevance of the proposed approach, numerical experiments are carried out on a 1D academic rod and a 3D aircraft fuselage-like structure.

Keywords

wave finite element method;periodic structures;band gaps;passive vibration control;aircraft fuselage;

Language

English

References

1.

Bennett, M. S. and Accorsi, M. L. (1994), "Free wave propagation in periodically ring stiffened cylindrical shell", J. Sound Vib., 171(1), 49-66.

2.

Doyle, J. F. (1997), Wave Propagation in Structures, 2nd Edition, Springer-Verlag, New York, NY, USA.

3.

Goffaux, C., Sánchez-Dehesa, J., Yeyati, A. L., Lambin, Ph., Khelif, A., Vasseur, J. O. and Djafari-Rouhani, B. (2002), "Evidence of Fano-like interference phenomena in locally resonant materials", Phys. Rev. Lett., 88(22), 225502.

4.

Goldstein, A.L., Silva, P.B. and Arruda, J.R.F. (2010), "The wave spectral finite element method applied to the design of periodic waveguides", Proceedings of the 18th International Congress on Sound and Vibration, Rio de Janeiro, Brazil, July.

5.

Kashina, V.I. and Tyutekin, V.V. (1990), "Waveguide vibration reduction of longitudinal and flexural modes by means of a multielement structure of resonators", Sov. Phys. Acoust., 36, 383-385.

6.

Kushwaha, M.S., Halevi, P., Dobrzynski, L. and Djafari-Rouhani, B. (1993), "Acoustic band structure of periodic elastic composites", Phys. Rev. Lett., 71(13), 2022-2025.

7.

Kushwaha, M.S., Halevi, P., Martinez, G., Dobrzynski, L. and Djafari-Rouhani, B. (1994), "Theory of acoustic band structure of periodic elastic composites", Phys. Rev. B., 49(4), 2313-2322.

8.

Lee, S., Vlahopoulos, N. and Waas, A.M. (2010), "Analysis of wave propagation in a thin composite cylinder with periodic axial and ring stiffeners using periodic structure theory", J. Sound Vib., 329(16), 3304-3318.

9.

Liu, Z., Zhang, X., Mao, Y., Zhu, Y.Y., Yang, Z., Chan, C.T. and Sheng, P. (2000), "Locally resonant sonic materials", Science, 289(5485), 1734-1736.

10.

Mencik, J.M. (2010), "On the low-and mid-frequency forced response of elastic structures using wave finite elements with one-dimensional propagation", Comput. Struct., 88(11-12), 674-689.

11.

Mencik, J.M. (2014), "New advances in the forced response computation of periodic structures using the wave finite element (WFE) method", Comput. Mech., 54(3), 789-801.

12.

Mencik, J.M. and Ichchou, M.N. (2005), "Multi-mode propagation and diffusion in structures through finite elements", Eur. J. Mech. A/Solid., 24(5), 877-898.

13.

Ormondroyd, J. and den Hartog, J.P. (1928), "The theory of the dynamic vibration absorber", T. Am. Soc. Mech. Eng., 50, A9-A22.

14.

Sigalas, M.M. and Economou, E.N. (1992), "Elastic and acoustic wave band structure", J. Sound Vib., 158(2), 377-382.

15.

Sigalas, M.M., Kushwaha, M.S., Economou, E.N., Kafesaki, M., Psarobas, I.E. and Steurer, W. (2005), "Classical vibrational modes in phononic lattices: theory and experiment", Z. Kristallogr., 220, 765-809.

16.

Silva, P.B., Mencik, J.M. and Arruda, J.R.F. (2014), "On the forced harmonic response of coupled systems via a WFE-based super-element approach", Proceedings of the International Conference on Noise and Vibration Engineering (ISMA), Leuven, Belgium, September.

17.

Silva, P.B., Mencik, J.M. and Arruda, J.R.F. (2015), "Wave finite element based super-elements for forced response analysis of coupled systems via dynamic substructuring", Int. J. Numer. Meth. Eng., doi: 10.1002/nme.5176.

18.

Sorokin, S.V. and Ershova, O.A. (2004), "Plane wave propagation and frequency band gaps in periodic plates and cylindrical shells with and without heavy fluid loading", New J. Phys., 278(3), 501-526.

19.

Thompson, D.J. (2008), "A continuous damped vibration absorber to reduce broad-band wave propagation in beams", J. Sound Vib., 311, 824-842.

20.

Wang, Z., Zhang, P. and Zhang, Y. (2013), "Locally resonant band gaps in flexural vibrations of a Timoshenko beam with periodically attached multioscillators", Math. Probl. Eng., 2013 (Article ID 146975), 10.

21.

Xiao, Y., Mace, B.R., Wen, J. and Wen, X. (2011), "Formation and coupling of band gaps in a locally resonant elastic system comprising a string with attached resonators", Phys. Lett. A, 375, 1485-1491.

22.

Xiao, Y., Wen, J. and Wen, X. (2012), "Longitudinal wave band gaps in metamaterial-based elastic rods containing multi-degree-of-freedom resonators", New J. Phys., 14, 033042.