Coupling FEM, Bloch Waves and TMM in Meta Poroelastic Laminates
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: 01 March 2018
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