A wave based method to predict the absorption, reflection and transmission coefficient of two-dimensional rigid frame porous structures with periodic inclusions

Abstract

This paper presents an extension to the Wave Based Method to predict the absorption, reflection and transmission coefficients of a porous material with an embedded periodic set of inclusions. The porous unit cell is described using the Multi-Level methodology and by embedding Bloch-Floquet periodicity conditions in the weighted residual scheme.The dynamic pressure field in the semi-infinite acoustic domains is approximated using a novel wave function set that fulfills the Helmholtz equation, the Bloch-Floquet periodicity conditions and the Sommerfeld radiation condition. The method is meshless and computationally efficient, which makes it well suited for optimisation studies.

Prediction of transmission, reflection and absorption coefficients of periodic structures using a hybrid Wave Based – Finite Element unit cell method

“…The minimisation of boundary conditions ( 3) and ( 4)-( 7) in the next step would involve the integration of residuals on infinitely large surfaces. In order to avoid these issues, the wave functions in the semi-unbounded acoustic domains are selected to fulfill the Helmholtz equation ( 2), the Sommerfeld radiation condition (3) and the Bloch-Floquet conditions ( 4)-(7 a priori), similarly as in the corresponding 2D case [44]. The wave functions Φ (α) w (r) for a semi-unbounded periodic domain are based on a plane wave expansion:…”

“…This method is very effective, but breaks down when higher order acoustic Bloch-Floquet modes have to be accounted for. The Wave Based Method (WBM) [44] and the Multipole Method [45], have been applied to predict absorption, reflection and transmission coefficients of porous and poro-elastic layers with periodic inclusions, explicitly accounting for the vibro-acoustic coupling between the UC and the surrounding semi-infinite acoustic domains, however, yet only apply to relatively simple geometries and are validated so far only for twodimensional simulations. The Finite Element Method [46] allows to model a unit cell involving a high geometrical complexity and any type of physics involved.…”

“…To analyse the vibro-acoustic response of periodic materials consisting of arbitrarily complex UCs, this paper proposes a hybrid Wave Based -Finite Element Unit Cell model as an extension of the WBM [44], also towards three-dimensional applications. The dynamic fields within the bounded UC are modelled with the Finite Element Method (FEM), allowing a high geometrical flexibility and arbitrary physics to be included.…”

Effect of pore connectivity on reflection amplitudes of an inhomogeneous wave in a composite porous solid saturated by two immiscible fluids

“…Starting with the classical work of Geertsma and Smith (1961), the study of reflection and transmission of waves still continues due to its increasing applicability and academic interest. Recently, the study conducted by Zhao and Shen (2015) and Deckers et al (2016) is worth mentioning in this regard. The present work studies the effect of pore connection on the reflection and transmission of an inhomogeneous wave striking at the interface of two dissimilar porous media.…”

A polynomial‐based method for topology optimization of phononic crystals with unknown‐but‐bounded parameters

“…In the frequency range of BG, the propagation of acoustic/elastic wave is directional forbidden (the directional BG) or totally forbidden (the full BG) . Unique phenomena, for instance, acoustic/elastic filtering or blocking,() acoustic mirrors, and acoustic/elastic cloaking,() have been experimentally observed or theoretically demonstrated in recent years. () A deep research of the band structures and BGs will significantly help us to understand the propagation of acoustic/elastic wave in PnCs and then to design the acoustic/elastic wave devices.…”