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Sound transmission through double-walls

When a sound wave strikes a partition, some portion of its energy is reflected, another portion is absorbed and the remaining portion is transmitted through (see figure 1.5).
The amounts of reflection, absorption and transmission depend upon the properties of the partition. A partition can be any panel or any combination of panels or panels with sound packages. A sound package may be sound absorbent materials, or material attachments to panels for stiffening, absorption and/or damping purposes. There is hence a vast variety of partitions that are available and one single theory cannot adequately describe the sound transmission characteristics. Aircraft fuselage, trim panel, noise treatment materials in between the fuselage and trim panel, structural links and windows all make up the partition that separates the interior of the aircraft from the outside.

Compression effects on the acoustic performance of porous materials

During installation, the thermal and acoustic insulation present in aircraft cockpit can be submitted to a certain degree of compression and the effects related to its acoustical performance have to be studied. Castagnède et al. [95] describe the effect of compression on the absorption coefficient of porous materials by developing some heuristic formulas to predict the evolution of porous materials properties with compression. Results show that resistivity and tortuosity tend to increase with compression while porosity and characteristics lengths tend to decrease (a definition of the porous material properties can be found in [5]). The material is modelled as an equivalent fluid [5, 96–101] and different equations are proposed for a 1D or a 2D compression. The assumed hypotheses are that the acoustic incident field is normal to the material surface, the material is supposed to have a fibrous network, the fibres are supposed not experiencing any deformation during the compression and keep their initial radius unchanged and the compression rate is close to one (defined as the ratio between nominal and compressed thickness).

Paper published on the Applied Acoustics Journal

Acoustic comfort has become a high priority in automotive, building and aeronautical structures subjected to noise. Passive acoustic treatments such as porous materials [5], diffusers [120, 121], acoustic and membrane resonators [122, 123] have been constantly studied and optimized in terms of acoustical properties and reduction of mass, in order to fit modern industrial constrains. This paper treats of compression effects on porous materials. During installation such materials can be subjected to a certain degree of compression, with consequent changes in their frame properties and thickness. In aeronautical applications, as the context of the present research, compression can result from the installation of equipment, cables and ventilation grids. It is thus non-uniform and changes locally the properties of the sound package. This may impact the targeted efficiency of the treatment. Castagnède et al. [95, 102] has proposed simple formulas to modify the material properties to account for the influence of uniform compression on the absorption coefficient. Their work was limited to fibrous and felt materials. Wang et al. [103] has applied their formulation using an elastic approach for the material. However, a similar study related to the transmission loss (TL) has not been performed. This is the subject of the present work.
The studied material is a glass wool and the effect of its frame compression on the TL of a structure composed of an isotropic plate lined with a porous layer is investigated both analytically and experimentally. First, the theoretical aspects of sound propagation and compression of porous materials are introduced in section 2. Section 3 presents the test structure and describes the experimental procedure to obtain its TL. The experimental and theoretical results are compared and discussed in section 4. Finally, the effect of compression on the TL is analysed in terms of variations in porous properties, radiation efficiency and wave-number.

Modelling sound absorbing materials

Poroelastic materials may be modeled using an equivalent fluid approach under the assumption that the solid phase is either rigid [5, 96–98] or limp [99–101]. Without these assumptions, Biot’s model is required [5, 104, 105].
In Biot’s model, the poroelastic medium is described by the macroscopic displacement of solid and fluid phases represented by us and uf , respectively. One shear and two compression waves propagate in the poroelastic medium. The expressions of the three wave numbers are given in Appendix 2.8. The two equations of movement form the following coupled system [5].

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Effects of compression on porous physical parameters

The theory presented in this section has been extracted from papers [95, 102, 103] treating the compression of fibrous materials. The compression rate (n) is defined as: n = h0 h , where h0 and h are the nominal and the compressed thickness, respectively. Since only the compression case is presented in this paper, n is greater than 1. The anisotropy effect during compression is not taken into account.
For a low compression rate, simple heuristic formulas have been proposed by Castagnède et al. [95, 102] to characterize compression of the fibrous network in terms of variations in material properties. The material is modelled as an equivalent fluid. Different equations are proposed for a uniaxial and surface-like compression. Variations in flow resistivity, porosity and characteristic lengths are calculated theoretically while variations in the tortuosity are determined from ultrasonic measurements.
The assumed hypotheses are as follows: the incident acoustical field is normal to the material surface. The material is supposed to have a fibrous network, the fibres of which are not supposed to experience any deformation during the compression of the material. Their initial radius remains unchanged and the compression rate is close to one.

Table of contents :

1.1 Industrial context
1.2 Objectives
1.3 Literature review
1.3.1 Aircraft interior noise: sources and control treatments
1.3.2 Vibroacoustics of aircraft panels
1.3.3 Sound transmission through double-walls
1.3.4 Compression effects on the acoustic performance of porous materials
1.3.5 Vibration isolating mounts
1.4 Summary and methodology
2.1 Chapter introduction
2.2 Résumé de l’article publié dans le journal Applied Acoustics
2.3 Paper published on the Applied Acoustics Journal – Introduction
2.4 Theory
2.4.1 Modelling sound absorbing materials
2.4.2 Effects of compression on porous physical parameters
2.4.3 Sound transmission through multilayer structures
2.5 Description of the experiment
2.6 Results and discussion
2.6.1 Influence of compression on the TL response
2.6.2 Influence of fibrous properties on the TL
2.6.3 Influence of compression on the radiation efficiency
2.7 Conclusion
2.8 Appendix: Modelling sound absorbing materials (complementary theory) .
3.1 Chapter introduction
3.2 Résumé de l’article publié dans le journal NCEJ
3.3 Paper published on the NCEJ Journal – Introduction
3.4 Theory
3.4.1 SEA modelling of a double-wall
3.4.2 Isolator modelling and structural coupling loss factor determination
3.5 Description of the experiments
3.5.1 Measurement of isolator’s dynamic stiffness
3.5.2 SEA measurements on a double-wall
3.6 Results and discussion
3.6.1 Isolator dynamic stiffness
3.6.2 Results in configuration 1
3.6.3 Results in configuration 2
3.7 Conclusion
4.1 Chapter introduction
4.2 Résumé de l’article soumis au journal Acta Acustica united with Acustica .
4.3 Paper submitted to Acta Acustica United with Acustica Journal – Introduction
4.4 Theory
4.4.1 Transfer matrix method (TMM)
4.4.2 Statistical energy analysis (SEA)
4.5 Description of the measurements
4.5.1 Description of the systems
4.5.2 Damping loss factor
4.5.3 Modal density
4.5.4 Radiation efficiency
4.5.5 Transmission loss
4.6 Results and discussion
4.6.1 Modal density
4.6.2 Radiation efficiency
4.6.3 Transmission loss comparisons between TMM, SEA and measurements
4.7 Conclusion
4.8 Supplementary analysis on academic double-walls
5.1 Chapter introduction
5.2 Double-wall SEA modelling under acoustic excitation (diffuse field)
5.2.1 Résumé de l’article à être soumis au Journal of the Acoustic society of America
5.2.2 Paper to be submitted to the Journal of the Acoustical Society of America – Introduction
5.2.3 Theory
5.2.4 Description of the experiments
5.2.5 Results and discussion
5.2.6 Conclusion
5.3 Double-wall SEA modelling under structural excitation (uncorrelated point forces)
A Principles for double-wall SEA modelling under aerodynamic excitation (turbulent boundary layer)


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