Wave Motion and Stop-Bands in Pipes with Helical Characteristics Using Wave Finite Element Analysis

Document Type: Research Paper

Authors

1 Dipartimento di Ingegneria e Architettura, Universita degli Studi di Parma, Viale delle Scienze 181/A, 43100 Parma, Italy

2 Department of Materials and Production, Aalborg University, Fibigerstraede 16, DK-9220 Aalborg East, Denmark

3 Vestas Wind Systems A/S, Hedeager 42, DK-8200 Aarhus North, Denmark

Abstract

Pipes are widely used in many industrial and mechanical applications and devices. Although there are many different constructions according to the specific application and device, these can show helical pattern, such as spiral pipes, wire-reinforced pipes/shells, spring-suspension, and so on. Theoretical modelling of wave propagation provides a prediction about the dynamic behavior, and it is fundamental in the design process of these structures/devices and in structural health monitoring techniques. However, standard approaches have limitations in terms of difficulties in modelling and impossible computational cost at higher frequencies. In this study, the wave characteristics in waveguides with helical patterns are obtained using a Wave Finite Element (WFE) method. The method is described for a 1D and 2D waveguide with helical properties and it is illustrated by numerical examples. These include the optimization of stop-bands for a fluid-filled pipe with concentrated masses and a cylindrical structure with helical orthotropy.

Keywords

Main Subjects

[1] Pearson, D., Dynamic behaviour of helical springs, The Shock and Vibration Digest, 20, 1988, pp. 3-9.

[2] Sorokin, S., Linear dynamics of elastic helical springs: Asymptotic analysis of wave propagation, Proceeding of the Royal Society A: Mathematical, Physical and Engineering Sciences, 465, 2009, pp.1513-1537.

[3] Maurin, E., Claeys, C., Van Belle, L., Desmet, W., Bloch theorem with revised boundary conditions applied to glide, screw and rotational symmetric structures, Computer Methods in Applied Mechanics and Engineering, 318, 2017, pp. 497-513.

[4] Lee, J., Thompson, D.J., Dynamic stiffness formulation, free vibration and wave motion of helical springs, Journal of Sound and Vibration, 239, 2001, pp. 297-320.

[5] Lee, J., Free vibration analysis of cylindrical helical springs by the pseudospectral method, Journal of Sound and Vibration, 302, 2007, pp. 185-196.

[6] Sorokin, S., The Green’s matrix and the boundary integral equations for analysis of time-harmonic dynamics of elastic helical springs, Journal of the Acoustical Society of America, 129, 2011, pp. 1315-1323.

[7] Treyssède, F., Numerical investigation of elastic modes of propagation in helical waveguides, The Journal of the Acoustical Society of America, 121, 2007, pp. 3398–3408.

[8] Treyssède, F., Elastic waves in helical waveguides, Wave Motion, 45, 2008, pp. 457-470.

[9] Liu, Y., Han, Q., Li, C., Huang, H., Numerical investigation of dispersion relations for helical waveguides using the Scaled Boundary Finite Element Method, Journal of Sound and Vibration, 333, 2014, pp. 1991-2002.

[10] Renno, J.M., Mace, B.R., Vibration modelling of helical springs with non-uniform ends, Journal of Sound and Vibration, 331, 2012, pp. 2809-2823.

[11] Paganini, L., Manconi, E., Søe-Knudsen, A., Sorokin, S., Optimum design of a periodic pipe filter using waves and finite elements, EURODYN 2011, Eighth International Conference on Structural Dynamics, Leuven, Belgium, 4-6 July 2011.

[12] Manconi, E., Sorokin, S., Garziera, R., Wave propagation in pipes with helical patterns, COMPDYN 2017, 6th ECCOMAS thematic conference on computational methods in structural dynamics and earthquakes engineering, Rhodes Island, Greece, 17-17 June 2017.

[13] Mace, B., Duhamel, D., Brennan, M., Hinke, L., Finite element prediction of wave motion in structural waveguides, Journal of the Acoustical Society of America, 117, 2005, pp. 2835-2843.

[14] Manconi, E., Mace, B.R., Wave characterization of cylindrical and curved panels using a finite element method, Journal of the Acoustical Society of America, 125, 2009, pp. 154-163.

[15] Waki, Y., Mace, B.R., Brennan, M.J., Numerical issues concerning the wave and finite element method for free and forced vibrations of waveguides, Journal of Sound and Vibration, 327, 2009, pp. 92-108.

[16] Søe-Knudsen, A., Sorokin S., On accuracy of the wave finite element predictions of wavenumbers and power flow: A benchmark problem, Journal of Sound and Vibration, 330, 2001, pp. 2694-2700.

[17] Manconi, E., Mace, B.R., Estimation of the loss factor of viscoelastic laminated panels from finite element analysis, Journal of Sound and Vibration, 329, 2010, pp. 3928-3939.

[18] Manconi, E., Mace, B.R., Garziera, R., Wave finite element analysis of fluid-filled pipes, NOVEM 2009, Noise and Vibration: Emerging Methods, Oxford, UK, 05-08 Apr 2009.

[19] Manconi, E., Mace, B.R., Garziera, R., The loss-factor of pre-stressed laminated curved panels and cylinders using a wave and finite element method, Journal of Sound and Vibration, 332, 2014, pp. 1704-1711.

[20] Renno, J.M., Mace, B.R., Calculating the forced response of two-dimensional homogeneous media using the wave and finite element method, Journal of Sound and Vibration, 330, 2011, pp. 5913-5927.

[21] Mitrou, G., Ferguson, N., Renno, J., Wave transmission through two-dimensional structures by the hybrid FE/WFE approach, Journal of Sound and Vibration, 389, 2017, pp. 484-501.

[22] Zhong, W.X., Williams, F.W., On the direct solution of wave propagation for repetitive structures, Journal of Sound and Vibration, 181, 1995, pp. 485-501.

[23] Shen, M.R., Cao, W.W., Acoustic bandgap formation in a periodic structure with multilayer unit cells, Journal of Physics D-Applied Physics, 33, 2000, pp. 1150-1154.

[24] Domadiya, P.G., Manconi, E., Vanali, M., Andersen, L.V., Ricci, A., Numerical and experimental investigation of stop-bands in finite and infinite periodic one-dimensional structures, Journal of Vibration and Control, 22, 2014, pp. 920-931.

[25] Søe-Knudsen, A., Design of stop-band filter by use of curved pipe segments and shape optimization, Journal Structural and Multidisciplinary Optimization archive, 44, 2011, pp. 863-874.

[26] Auld, B.A., Acoustic fields and waves in solids, Krieger Publishing Company, Malabar, FL,1990.

[27] Price, W.L., Global optimization by controlled random search, Journal of Optimization Theory and Applications, 40, 1983, pp. 333-347.