This work deals with the study of a plane periodic multilayer structure in which the elementary stack consists of two plates in contact: one in aluminum (AL) and the other one in polyethylene (PE). These isotropic materials, present a high acoustic impedance contrast. The attenuation of the longitudinal and transverse waves is taken into account in the polyethylene but neglected in the aluminum plate. The effect of different defects is analyzed. Firstly, we focus on the effect of the presence of grease inclusion in the polyethylene plate (considering the two plates of the elementary stack in perfect contact). Secondly, the effect of disbond simulated by the insertion of a thin Teflon layer between the interfaces of the two layers constituting the elementary stack of the multilayer structure is investigated. Finally, the effect of the stacking sequences of the multilayer is analyzed. In order to obtain the effective acoustic parameters of polyethylene layer, allowing to evaluate the reflection and transmission coefficients using the stiffness matrix method developed by Rokhlin etal., four homogenization models are analyzed, then the best one to our configuration is chosen. The comparison of the simulation results is carried out.
References
[1]
Khelif, A., Choujaa, A., Djafari-Rouhani, B., Wilm, M., Ballandras, S. and Laude, V. (2003) Trapping and Guiding of Acoustic Waves by Defect Modes in a Full-Band- Gap Ultrasonic Crystal. Physical Review B, 68, Article No. 214301. https://doi.org/10.1103/PhysRevB.68.214301
[2]
Perez, S., Caballero, J.V., Martinez-Sala, R., Rubio, C., Sanchezdehesa, J., Meseguer, F., Llinares, J. and Galvez, F. (1998) Sound Attenuation by a Two-Dimensional Array of Rigid Cylinders. Physical Review Letters, 80, Article No. 5325. https://doi.org/10.1103/PhysRevLett.80.5325
[3]
Rokhlin, S.I. and Wang, L. (2002) Stable Recursive Algorithm for Elastic Wave Propagation in Layered Anisotropic Media: Stiffness matrix Method. The Journal of the Acoustical Society of America, 112, 822-834. https://doi.org/10.1121/1.1497365
[4]
Lenoir, O. and Maréchal, P. (2009) Study of Plane Periodic Multilayered Viscoelastic Media: Experiment and Simulation. IEEE International Ultrasonics Symposium Proceedings, Rome, 20-23 September 2009, 1028-1031. https://doi.org/10.1109/ULTSYM.2009.5441518
[5]
Lenoir, O., Maréchal, P. and Rembert, P. (2009) Study of Period and Structure Modes of Periodic Multilayers with the S Matrix Formalism. 19ème Congrès Français de Mécanique, Marseille, 24-28 August 2009, 6 p.
[6]
Siryabe, E., Ntamack, G. and Maréchal, P. (2013) Holes Effects in Plane Periodic Multilayered Viscoelastic Media. Open Journal of Acoustics, 3, 80-87. https://doi.org/10.4236/oja.2013.33013
[7]
Maréchal, P., Lenoir, O., Khaled, A., Ech Cherif El Kettani, M. and Chenouni, D. (2014) Viscoelasticity Effect on a Periodic Plane Medium Immersed in Water. Acta Acustica United with Acustica, 100, 1036-1043. https://doi.org/10.3813/AAA.918783
[8]
Maréchal, P. and Lenoir, O. (2010) Effets de dépériodisation dans une structure multicouche plane viscoélastique: expérience et simulation. 10ème Congrès Français d’Acoustique, Lyon, 12-16 April, 2010, 6 p. https://hal.archives-ouvertes.fr/hal-00541707/document
[9]
Lenoir, O., Khaled, A., Marechal, P. and Chenouni, D. (2012) Effects of a Default on the Reflectivity of Plane Periodic Media. Proceedings of the Acoustics, Nantes, 23-27 April 2012, 271-276.
[10]
Khaled, A., Elamri, F.-Z., El Kadmiri, I. and Bria, D. (2019) Effects of Defect Layers Insertion on the Transmission of a Submerged One-Dimensional Phononic Structure. International Conference on Wireless Technologies, Embedded and Intelligent Systems, Fez, Morocco, 3-4 April 2019, 1-6. https://doi.org/10.1109/WITS.2019.8723782
[11]
Magoariec, H. (2003) Adaptation élastoplastique et homogénéisation périodique. Ph.D. Thesis, Aix-Marseille II University, Marseille.
[12]
Caloz, C. and Itoh, T. (2006) Electromagnetic Metamaterials: Transmission Line Theory and Microwave Applications: The Engineering Approach. Wiley & IEEE Press, Hoboken, NJ. https://doi.org/10.1002/0471754323
[13]
Gaunaurd, G., Callen, E. and Barlow, J. (1984) Pressure Effects on the Dynamic Effective Properties of Resonating Perforated Elastomers. The Journal of the Acoustical Society of America, 76, 173-177. https://doi.org/10.1121/1.391090
[14]
Hashin, Z. and Shtrikman, S. (1963) A Variational Approach to the Theory of the Elastic Behaviour of Multiphase Materials. Journal of the Mechanics and Physics of Solids, 11, 127-140. https://doi.org/10.1016/0022-5096(63)90060-7
[15]
Hashin, Z. (1965) On Elastic Behaviour of Fibre Reinforced Materials of Arbitrary Transverse Phase Geometry. Journal of the Mechanics and Physics of Solids, 13, 119- 134. https://doi.org/10.1016/0022-5096(65)90015-3
[16]
Wang, L. and Rokhlin, S.I. (2001) Stable Reformulation of Transfer Matrix Method for Wave Propagation in Layered Anisotropic Media. Ultrasonics, 39, 413-424. https://doi.org/10.1016/S0041-624X(01)00082-8
