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Coupling FEM, Bloch Waves and TMM in Meta Poroelastic Laminates


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The propagation of airborne plane waves in the presence of a meta poroelastic laminate, that is a poroelastic matrix coated with thin elastic layers at its facings and periodically-embedded with inclusions, is studied. Using the Finite Element Method (FEM) only would result in a drastic increase of the degrees of freedom due to the fine mesh required to account for the very thin coatings. Here, the approach relies on: the Bloch wave expansion of the fields in air; the modal Transfer Matrix Method to account for the coatings; and the coupling with the FEM model of the poroelastic matrix and the resonant inclusions. The model is developed for reflection and transmission problems and it can account for coatings with multiple layers. The procedure induces the addition of the Bloch coefficients in the FEM's linear system at a negligible additional computational cost. It is applied to the meta poroelastic laminates with poroelastic inclusions and rubber shell inclusions. The results are compared with those from the Multiple Scattering Theory and an excellent agreement between the methods is found. The approach offers a numerically-efficient way to account for coatings applied to meta poroelastic layers, and finds applications in industrial prototypes where coatings are widely used.

Document Type: Research Article

Publication date: March 1, 2018

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  • Acta Acustica united with Acustica, published together with the European Acoustics Association (EAA), is an international, peer-reviewed journal on acoustics. It publishes original articles on all subjects in the field of acoustics, such as general linear acoustics, nonlinear acoustics, macrosonics, flow acoustics, atmospheric sound, underwater sound, ultrasonics, physical acoustics, structural acoustics, noise control, active control, environmental noise, building acoustics, room acoustics, acoustic materials, acoustic signal processing, computational and numerical acoustics, hearing, audiology and psychoacoustics, speech, musical acoustics, electroacoustics, auditory quality of systems. It reports on original scientific research in acoustics and on engineering applications. The journal considers scientific papers, technical and applied papers, book reviews, short communications, doctoral thesis abstracts, etc. In irregular intervals also special issues and review articles are published.
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