Computation of dispersion diagrams for periodic porous materials modeled as equivalent fluids

Magliacano, Dario; Ouisse, Morvan; Khelif, Abdelkrim; Rosa, Sergio De; Franco, Francesco; Atalla, Noureddine; Collet, Manuel

doi:10.1016/j.ymssp.2020.106749

Cited by 22 publications

(13 citation statements)

References 22 publications

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“…For each physical property of the system, the periodicity is described by α(x − rn) − α(x) = 0, where α is a generic physical property, n is a vector of integers normal to the face considered, r = (r 1 ; r 2 ; r 3 ) is a matrix containing the three vectors defining the cell periodicity directions and lengths, and Ω is the domain of interest. This applies everywhere except on the discontinuity surfaces, where appropriate boundary conditions apply [19]. By further developing the latter equation and applying the Bloch theorem [29], which extends Floquet's theory to 3D systems, one obtains:…”

Section: Shift Cell Operator Technique 221 Introductionmentioning

confidence: 99%

“…In this context, the present work investigates the application of the shift cell approach to poroelastic media; this allows to obtain dispersion characteristics of frequencydependent damped materials through the resolution of a quadratic eigenvalue problem, whose accuracy only depends on the FEM meshing. This technique has already been successfully applied to describe the mechanical behavior of periodic structures embedding visco-elastic materials [16,17], piezoelectric materials [18] and foams modeled as equivalent fluids [19]. The main novelty of the present work consists in the formulation and application of the shift cell technique to Biot-modeled poro-elastic media.…”

Section: Introductionmentioning

confidence: 99%

“…Indeed, even if the usage of Floquet-Bloch (F-B) periodic conditions actually allows it, a very powerful non-linear solver is required in that case. The shift cell operator [16,19], instead, leads to a quadratic eigenvalue problem even in the presence of frequency-dependences and/or damping. The main mathematical difference with respect to the classical F-B approach is that, in the case of the shift cell operator, the phase shift of the boundary conditions and the exponential amplitude decrease, related to wave propagation, are integrated into the partial derivative operator.…”

Section: Shift Cell Operator Technique 221 Introductionmentioning

confidence: 99%

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Formulation and validation of the shift cell technique for acoustic applications of poro-elastic materials described by the Biot theory

Magliacano

Ashani

Ouisse

et al. 2021

Mechanical Systems and Signal Processing

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The inclusion of vibroacoustic treatments at early stage of product development through the use of poro-elastic media with periodic inclusions, which exhibit proper dynamic filtering effects, is a powerful strategy for the achievement of lightweight sound packages and represents a convenient solution for manufacturing aspects. This can have different applications in transportation (aerospace, automotive, railway), energy and civil engineering fields, where weight, space and vibroacoustic comfort are still critical challenges. This paper develops the shift cell operator approach as a numerical tool to investigate the dispersion characteristics of periodic poro-elastic media. It belongs to the class of the k(ω) (wave number as a function of the angular frequency) methods and leads to a quadratic eigenvalue problem, even when considering frequency-dependent materials, contrarily to the ω(k) approach that would lead to a non-linear eigenvalue problem for frequency-dependent materials.

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Section: Shift Cell Operator Technique 221 Introductionmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

Section: Shift Cell Operator Technique 221 Introductionmentioning

confidence: 99%

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Formulation and validation of the shift cell technique for acoustic applications of poro-elastic materials described by the Biot theory

Magliacano

Ashani

Ouisse

et al. 2021

Mechanical Systems and Signal Processing

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“…In the work by Groby et al [7], the influence of periodic inclusions on the acoustic performances is explained by excitation of additional acoustic modes which dissipate acoustic energy. To this aim, advanced and innovative numerical tools are more and more useful [16]. Periodic poro-elastic media, generated by uniform spatial repetition of specifically designed unit cells in the 3D domain, are extensively used in noise control applications; examples include polyurethane foams, metal foams, porous asphalt, cotton, hemp synthetic fibers, jute, glass wools, which are widely used in commercial and industrial applications [17].…”

Section: Introductionmentioning

confidence: 99%

Computation of acoustic properties and design guidelines of periodic Biot-modeled foams

et al. 2020

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This paper aims at consolidating research dealing with vibroacoustics of periodic media. The main goal of this work is to develop and to validate tools for the design of global vibroacoustic treatments based on periodic patterns, allowing passive control of acoustic paths in layered concepts. To this aim, some enhancements are introduced to the state of the art on the the study and the design of Biot-modeled foams, in order to obtain desired acoustics performances through embedded periodic inclusions. At first, the properties of the studied acoustic package, constituted by a poro-elastic 3D unit cell, is introduced. Successively, through the use of the acoustic-structure coupling that comes from the implementation of Biot model, a non-rigid inclusion test campaign is carried out by considering some solid (but still nonperfectly-rigid) inclusions in a 3D-modeled unit cell; in particular, six setups are discussed herein. Then, some design guidelines are provided in order to predict at which frequency the first performance peak appears, together with its amplitude, as functions of unit cell dimensions, airflow resistivity, tortuosity, viscous and thermal characteristic lengths, frame density, Young modulus and loss factor; conversely, it is shown also the link between the unit cell dimensions and the first performance peak amplitude as functions of the design frequency.

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“…Porous media are widely used in such fields as resource development engineering, farmland water conservancy engineering, chemical infiltration, biological tissue, etc [1][2][3]. In order to simplify mathematical calculations and more vividly represent the pore space of porous media, physical models are usually used to replace complex pore space [4].…”

Section: Introductionmentioning

confidence: 99%

Study of Oil-Water Two-Phase Stratified Flow in Horizontal Fractures

Huang

Sun

et al. 2020

E3S Web Conf.

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The relative permeability of oil-water two-phase flow is an important parameter in fractured petroleum reservoirs. It is widely accepted that the sum of relative permeabilities is less than 1. In this study, a series of experiments have been conducted on six rectangular fractures for oil-water two-phase flows. Analytical investigations of the effects of flow rate, aspect ratio, and fracture size on the relative permeability of oil-water two-phase are analysed. Basic fluid flow equations are combined to develop a new analytical model for water-oil two-phase flow in a horizontal fracture. The simulation results predicted by this model are in good agreement with the experimental data. The relative permeability is a function of flow ratio, viscosity ratio, aspect ratio and saturation. It increases as aspect ratio increases if the fracture depths are the same, while it decreases as aspect ratio increases if the fracture widths are identical. Both experiment and model indicate that the sum of relative permeabilities of oil and water is greater than 1 in some cases, different from the accepted view.

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Computation of dispersion diagrams for periodic porous materials modeled as equivalent fluids

Cited by 22 publications

References 22 publications

Formulation and validation of the shift cell technique for acoustic applications of poro-elastic materials described by the Biot theory

Formulation and validation of the shift cell technique for acoustic applications of poro-elastic materials described by the Biot theory

Computation of acoustic properties and design guidelines of periodic Biot-modeled foams

Study of Oil-Water Two-Phase Stratified Flow in Horizontal Fractures

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