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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

has been cited by the following article:

• TITLE: Holes Effects in Plane Periodic Multilayered Viscoelastic Media

  AUTHORS: Emmanuel Siryabe, Guy-Edgar Ntamack, Pierre Maréchal

  KEYWORDS: Periodic Structures; Holes; Porosity; Phononic Crystal; Forbidden Bands; Transmission; Reflection; Attenuation

  JOURNAL NAME: Open Journal of Acoustics, Vol.3 No.3, September 9, 2013

  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.