The Wave Spectral Finite Element Method Applied To The Design Of Periodic Waveguides

The design of periodic layered structures with desired wave dispersion characteristics is a subject of great potential use in vibration isolation. In this work, the modelling of a onedimensional periodic layered structure is performed using the wave spectral finite element method (WSFEM). Wave spectral finite elements are developed based on post processing a short segment of the waveguide modelled with conventional structural finite elements. The dynamic stiffness spectral element matrices are developed for the different layered materials and applied to model the forced response of a finite periodic layered rod. The periodic rod is assumed to consist of a sequence of unit cells, each cell consisting of two layers of different materials with contrasting properties. The frequency spectrum of the periodic rod is determined by the layered structure layout, so that the periodic rod structure can be designed to have the desired band gap by adjusting the thickness of each layer and total number of cells. A periodic layered rod made of polyacetal and stainless steel was built and tested in order to validate the modelling results. Finally, in order to investigate the divergences between the simulated response by WSFEM and the experimental one, additional simulations were performed using conventional finite element analysis (FEA). Copyright © (2011) by the International Institute of Acoustics & Vibration.212441251Mencik, J.M., Ichchou, M.N., Multi-mode propagation and diffusion in structures through finite element (2005) European Journal of Mechanics A/Solids, 24, pp. 877-898Mace, B.R., Duhamel, D., Brennan, M.J., Hinke, L., Finite element prediction of wave motion in structural waveguides (2005) Journal of the Acoustical Society of America, 117 (5), pp. 2835-2843Mead, D.J., A general theory of harmonic wave propagation in linear periodic systems with multiple coupling (1973) Journal of Sound and Vibration, 27 (2), pp. 235-260Arruda, J.R.F., Nascimento, R.F., Building spectral elements from finite element models of waveguide slices (2008) Proceedings of the Ninth International Conference on Computational Structures Technology, , Stirlingshire, ScotlandDoyle, J.F., (1997) Wave Propagation in Structures, , 2nd. Edition, New York: SpringerArruda, J.R.F., Nascimento, R.F., Building spectral element dynamic matrices using finite element models of waveguide slices (2009) Proceeding of the NOVEM 2009, Noise and Vibration: Emerging Methods, , OxfordWaki, Y., Mace, B.R., Brennan, M.R., Free and forced vibrations of a tyre using a wave/finite element approach (2009) Journal of Sound and Vibration, 323, pp. 737-756Brillouin, L., (1953) Wave Propagation in Periodic Structures, , 2nd edn. New York: DoverSigalas, M., Economou, E., Elastic and acoustic wave band structure (1992) Journal of Sound and Vibration, 158, pp. 377-382Kushwaha, M.S., Classical band structure of periodic elastic composites (1996) International Journal of Modern Physics B, 10 (9), pp. 977-1094Sigmund, O., Jensen, J.S., Systematic design of phononic band-gap materials and structures by topology optimization (2003) Philosophical Transactions of the Royal Society A, 361, pp. 1001-1019Hussein, M.I., Hamza, K., Hulbert, R.A.G.M., Saitou, K., Multi-objective evolutionary optimization of periodic layered materials for desired wave dispersion characteristics (2006) Structural and Multidisciplinary Optimization, 31 (1), pp. 60-75Hussein, M.I., Hulbert, G.M., Scott, R.A., Dispersive elastodynamics of 1d banded materials and structures: Analysis (2006) Journal of Sound and Vibration, 289 (4-5), pp. 779-806Ewins, D.J., (1984) Modal Testing: Theory and Practice, , Research Studies Press LTD., Somerse