OJA  Vol.3 No.3 , September 2013
Holes Effects in Plane Periodic Multilayered Viscoelastic Media
Abstract: This work deals with the study of the reflection and transmission properties of plane periodic structures composed of N periods (1 ≤ N ≤ 3) in the MHz frequency range. The period consists of two bounded plates presenting a high acoustic impedance contrast one of which is in aluminum, the other is in polyethylene. The longitudinal and transversal attenuations are considered in polyethylene and neglected in aluminum. We take into account the case of emerging holes in the polyethylene layer. Simulations are based on the stiffness matrix method (SMM) developed by Rokhlin. When attenuation is considered in polyethylene, the reflection coefficients are different depending on the insonification side. The comparison of results without or with holes configurations are performed and showed that throughout holes allow the rapid observation of forbidden bands. The attenuation of the whole multilayer is also determined.
Cite this paper: E. Siryabe, G. Ntamack and P. Maréchal, "Holes Effects in Plane Periodic Multilayered Viscoelastic Media," Open Journal of Acoustics, Vol. 3 No. 3, 2013, pp. 80-87. doi: 10.4236/oja.2013.33013.

[1]   D. Maa, “Micro-Perforated-Panel Wideband Absorbers,” Noise Control Engineering Journal, Vol. 29, No. 3, 1987, pp. 77-84. doi:10.3397/1.2827694

[2]   F.-C. Lee and W.-H. Chen, “Acoustic Transmission Analysis of Multi-Layer Absorbers,” Journal of Sound and Vibration, Vol. 248, No. 4, 2001, pp. 621-634. doi:10.1006/jsvi.2001.3825

[3]   S. Hur, D. Lee and Y. Kwon, “A Study on the Sound Absorption Performance of Multiple Layer Perforated Plate Systems,” Proceedings of the KSME Spring Annual Conference, 2002, pp. 688-693.

[4]   A. Nilsson and B. Rasmussen, “Sound Absorption Properties of a Perforated Plate and Membrane Construction,” Acta Acustica United with Acustica, Vol. 57, No. 3, 1985, pp. 139-148.

[5]   X. Jing and X. Sun, “Experimental Investigations of Perforated Liners with Bias Flow,” Journal of the Acoustical Society of America, Vol. 106, No. 5, 1999, pp. 2436-2441. doi:10.1121/1.428128

[6]   C. Zwikker and C. Kosten, “Sound Absorbing Materials,” Elsevier Pub. Co., New York, 1949.

[7]   J. Kang and H. Fuchs, “Predicting the Absorption of Open Weave Textiles and Micro-Perforated Membranes Backed by an Air Space,” Journal of Sound and Vibration, Vol. 220, No. 5, 1999, pp. 905-920. doi:10.1006/jsvi.1998.1977

[8]   D. Lee and Y. Kwon, “Estimation of the Absorption Performance of Multiple Layer Perforated Panel Systems by Transfer Matrix Method,” Journal of Sound and Vibration, Vol. 278, No. 4-5, 2004, pp. 847-860. doi:10.1016/j.jsv.2003.10.017

[9]   O. Lenoir and P. Maréchal, “Study of Plane Periodic Multilayered Viscoelastic Media: Experiment and Simulation,” IEEE International Ultrasonics Symposium Proceedings, Rome, 20-23 September 2009, pp. 1028-1031. doi:10.1109/ultsym.2009.5441518

[10]   O. Lenoir, P. Maréchal, and P. Rembert, “Study of Period and Structure Modes of Periodic Multilayers with The S Matrix Formalism,” Congrès Fran?ais de Mécanique, Marseille, 2009.

[11]   P. Maréchal and O. Lenoir, “Effet de Déperiodisation dans une Structure Multicouche Plane Viscoélastique: Expérience et Simulation,” In : Société Fra?aise d’Acoustique SFA, Ed., 10 ème Congrès Fran?ais d’Acoustique, Lyon, 2010.

[12]   S. Rokhlin and L. Wang, “Stable Recursive Algorithm for Elastic Wave Propagation in Layered Anisotropic Media: Stiffness Matrix Method,” Journal of the Acoustical Society of America, Vol. 112, No. 3, 2002, pp. 822-834. doi:10.1121/1.1497365

[13]   P. Maréchal, L. Haumesser, L. Tran-Huu-Hue, J. Holc, D. Kuscer, M. Lethiecq and G. Feuillard, “Modeling of a High Frequency Ultrasonic Transducer Using Periodic Structures,” Ultrasonics, Vol. 48, No. 2, 2008, pp. 141- 149. doi:10.1016/j.ultras.2007.11.007

[14]   S. Ahmed and F. Jones, “A Review of Particulate Reinforcement Theories for Polymer Composites,” Journal of Materials Science, Vol. 25, No. 12, 1990, pp. 4933-4942. doi:10.1007/BF00580110

[15]   E. Garboczi and A. Day, “An Algorithm for Computing the Effective Linear Elastic Properties of Heterogeneous Materials: Three-Dimensional Results for Composites with Equal Phase Poisson Ratios,” Vol. 43, No. 9, 1995, pp. 1349-1362.

[16]   J. Poutet, D. Manzoni, F. Hage-Chehade, J.-F. Thovert and P. Adler, “The Effective Mechanical Properties of Random Porous Media,” Journal of the Mechanics and Physics of Solids, Vol. 44, No. 10, 1996, pp. 1587-1620. doi:10.1016/0022-5096(96)00051-8

[17]   S. Torquato, “Effective Stiffness Tensor of Composite Media: II. Applications to Isotropic Dispersions,” Journal of the Mechanics and Physics of Solids, Vol. 46, No. 8, 1998, pp. 1411-1440. doi:10.1016/S0022-5096(97)00083-5

[18]   K. Pithia, “An Approximate Calculation on the Elastic Constants of a Solid Containing Varying Volume Fractions of Cavities,” Physica A: Statistical Mechanics and its Applications, Vol. 222, No. , 1995, pp. 25-31.

[19]   A. Roberts and E. Garboczi, “Elastic Properties of Model Porous Ceramics,” Journal of the American Ceramic Society, Vol. 83, No. 12, 2000, pp. 3041-3048. doi:10.1111/j.1151-2916.2000.tb01680.x

[20]   S. Meille and E. Garboczi, “Linear Elastic Properties of 2D and 3D Models of Porous Materials Made from Elongated Objects,” Modelling and Simulation in Materials Science and Engineering, Vol. 9, No. 5, 2001, pp. 371- 390. doi:10.1088/0965-0393/9/5/303

[21]   M. Wang and N. Pan, “Elastic Property of Multiphase Composites with Random Microstructures,” Journal of Computational Physics, Vol. 228, No. 16, 2009, pp. 5978- 5988. doi:10.1016/

[22]   G. C. Gaunaurd and H. Uberall, “Resonance Theory of the Effective Properties of Perforated Solids,” Journal of the Acoustical Society of America, Vol. 71, No. 2, 1982, pp. 282-295. doi:10.1121/1.387452

[23]   G. Gaunaurd, E. Callen and J. Barlow, “Pressure Effects on the Dynamic Effective Properties of Resonating Perforated Elastomers,” Journal of the Acoustical Society of America, Vol. 76, No. 1, 1984, pp. 173-177. doi:10.1121/1.391090

[24]   Z. Hashin and S. Shtrikman, “A Variational Approach to the Theory of the Elastic Behaviour of Multiphase Materials,” Journal of the Mechanics and Physics of Solids, Vol. 11, No. 2, 1963, pp. 127-140. doi:10.1016/0022-5096(63)90060-7

[25]   Z. Hashin, “On Elastic Behaviour of Fibre Reinforced Materials of Arbitrary Transverse Phase Geometry,” Journal of the Mechanics and Physics of Solids, Vol. 13, No. 3, 1965, pp. 119-134. doi:10.1016/0022-5096(65)90015-3

[26]   Z. Hashin, “Analysis of Composite Materials—A Survey,” Journal of Applied Mechanics, Vol. 50, No. 3, 1983, pp. 481-505. doi:10.1115/1.3167081

[27]   C. H. Arns, M. A. Knackstedt, W. V. Pinczewski and E. J. Garboczi, “Computation of Linear Elastic Properties from Microtomographic Images: Methodology and Agreement between Theory and Experiment,” Geophysics, Vol. 67, No. 5, 2002, pp. 1396-1405. doi:10.1190/1.1512785

[28]   C. Hsieh, W. Tuan and T. Wu, “Elastic Behaviour of a Model Two-Phase Material,” Journal of the European Ceramic Society, Vol. 24, No. 15-16, 2004, pp. 3789-3793. doi:10.1016/j.jeurceramsoc.2004.02.002

[29]   C. Hsieh and W. Tuan, “Elastic Properties of Ceramic- Metal Particulate Composites,” Materials Science and Engineering: A, Vol. 393, No. , 2005, pp. 133-139. doi:10.1016/j.msea.2004.10.009

[30]   H. Hu, L. Onyebueke and A. Abatan, “Characterizing and Modeling Mechanical Properties of Nanocomposites— Review and Evaluation,” Journal of Minerals & Materials Characterization & Engineering, Vol. 9, No. 4, 2010, pp. 275-319.

[31]   H. Franklin, E. Danila and J. Conoir, “S-Matrix Theory Applied to Acoustic Scattering by Asymmetrically Fluid- Loaded Elastic Isotropic Plates,” Journal of the Acoustical Society of America, Vol. 110, No. 1, 2001, pp. 243- 253. doi:10.1121/1.1373636