MECH9325 Fundamentals of Acoustics and Noise
Assignment – Acoustic performance of a coating with inclusions
Part 2 due Monday 21 April 5pm (Moodle online submission)
Aim
In the first part of this assignment, you numerically modelled a multilayered homogeneous material comprising multiple layers of the same PDMS material. The aim of this second part is to numerically model voids and/or hard scatterers embedded in the PDMS.
Background
Inclusions embedded within a soft material such as PDMS result in wave scattering at frequencies around the resonance frequency of the inclusions. Wave scattering facilitates the conversion of sound waves into shear waves which are effectively damped due to high shear damping of the soft material. Inclusions are typically voids or hard scatterers which have their own resonance characteristics. Voids exhibit monopole resonance associated with pulsating motion, while hard scatterers undergo translational motion at dipole resonance. At frequencies around the resonance frequency of the inclusions, the coating acts as an efficient sound absorber.
Theoretically, effective medium approximation theory can used to model the inclusions as homogenised layers with effective material and geometric properties. The PDMS material with inclusions then becomes a multilayered design composed of alternating layers of the homogeneous material (PDMS) and the homogenised layer of inclusions (characterised in terms of an effective length, an effective density, and an effective longitudinal modulus). From the effective properties, all the terms for the transfer matrix can be calculated. The sound transmission is then obtained using the transfer matrix method. However, this is beyond the scope of this assignment! For your interest, you can see the inclusions modelled as a homogenised layer and the use of the transfer matrix method in terms of the effective properties in the following references.
https://doi.org/10.1016/j.ijmecsci.2024.109587 see Figure 1 and Eq. (6)
https://doi.org/10.1016/j.wavemoti.2016.10.006see Figure 2 and Eq. (21)
https://doi.org/10.1016/j.apacoust.2020.107501 see Figure 2 and Eqs. (13)-(15)
Models
Use the single layer model from Part 1 as a base. Increase the cross-section dimension to 0.1m. Use the following material properties for PDMS and steel for the hard scatterer.
|
Material
|
PDMS
|
Steel
|
|
Density (kg/m3)
|
1000
|
7890
|
|
Longitudinal modulus (GPa)
|
2.26(1+0.02i)
|
283
|
|
Shear modulus (GPa)
|
0.006(1+0.3i)
|
80.77
|
Model 1
Model a spherical void of radius 0.015m in the centre of the PDMS slab, with water on the incidence and transmission sides of the PDMS. Obtain the absolute value for the reflection and transmission coefficients, and present your results as 2D plots as a function of frequency. You could compare your results with Figure 2 (left column) in https://doi.org/10.1121/10.0026357. Also obtain the displacement surface plot of the PDMS at the monopole resonance frequency (frequency of minimum transmission coefficient).
Model 2
Extend the PDMS slab to model two spherical voids with the centres separated by 0.1m. Obtain the absolute value for the reflection and transmission coefficients, and present your results as 2D plots as a function of frequency. You could compare your results with Figure 3 (left column) in
Model a hard steel sphere of radius 0.03m in the centre of the PDMS slab. Obtain the absolute value for the reflection and transmission coefficients, and present your results as 2D plots as a function of frequency. You could compare your results with Figure 2 (right column) in https://doi.org/10.1121/10.0026357. Also obtain the displacement surface plot of the PDMS at the dipole resonance frequency (frequency ofminimum transmission coefficient).
Model 4
Extend the PDMS slab to model two hard steel spheres with the centres separated by 0.1m. Obtain the absolute value for the reflection and transmission coefficients, and present your results as 2D plots as a function of frequency. You could compare your results with Figure 3 (right column) in
https://doi.org/10.1121/10.0026357
Poster
Provide your results in a one-page poster. Your poster should include an introduction, description of the numerical model, results and discussion. The poster should not be too detailed or busy. For example, the lecture slides for this course are visually much easier to read than the lecture notes. The presentation of a poster should aim to be similar to the lecture slides by using large font size, bullet points where possible, no large chunks of text and large clear figures with easy to read axis labels. Your poster can also include references in smaller font size.