4.2 Design of the noise shield demonstrator
4.2.2 MAM layer design
The acoustic treatment of the noise shield demonstrator is to be in-tegrated into the underside of the stiffened cover sheet. Therefore, it is reasonable to exploit the particular structure of the panel for the design and integration of the MAM layers. In Fig. 4.3(a) it can be seen that the frames and stringers subdivide the cover sheet underside into rectangular bays. Skipping every second stringer row and using the frames as lateral boundaries, as indicated by the red shaded rectangle in Fig. 4.3(a), the cover sheet is sectioned into 5×5 bays. In each of these bays a so-called MAM element containing multiple unit cells and layers of MAMs is fastened to the frame webs of the cover sheet. 25 of these MAM elements tiled along the cover sheet in this manner make up the acoustic treatment of the noise shield demonstrator.
The resulting length and width of the MAM elements are 430 mm and 490 mm, respectively. An aluminum lattice is used to hold the MAM layers. As shown in Fig. 4.4, the lattice consists of 20 mm× 20 mm U-beams welded together and subdividing the MAM element into 3×3 MAM unit cells. Attachment lugs are welded to the sides of the grid so that the MAM element can be attached to the frames of the cover sheet. The edge lengths of the unit cells are given by Lx = 137 mm and Ly = 117 mm, respectively. Thus, the aspect ratio of the MAM unit cells is Λ ≈ 1.17. The mass of a lattice element is
490 mm
430mm
20 mm Attachment lugs
Figure 4.4: MAM element grid for supporting the two MAM layers inside the noise shield demonstrator.
given byMG= 1 kg. This particular design for the MAM element grid is a compromise between the required sub-wavelength size of the MAM unit cells and the grid mass, which – for fixed beam properties – linearly scales with the number of unit cells. Additionally, these MAM elements are sized so that they can also be integrated into the side wall of the fuselage. This enables further investigations of MAMs as cabin lining elements for other sound reduction concepts.
The sameOrastick membrane material as in the experimental MAM unit cell investigations (see Sections 2.4 and 3.3) is used for the MAM elements of the noise shield demonstrator. The manufacturing proce-dure of the MAM elements is similar to the unit cell test samples, so that the same membrane prestress resultant ofTm = 200 N/m can be assumed. With these membrane properties, the nondimensional bend-ing stiffness for the noise shield MAMs is given byΞ = 1.5×10−6 and can be regarded as negligible. For ambient air conditions with ρ0 = 1.18 kg/m3 and c0= 343 m/s, the nondimensional speed of sound and characteristic impedance become ς0= 7.4 andZ0 = 12.9, respectively.
Compared to the other MAM configurations, which are summarized in Table 2.1,ς0 is identical to the values for the impedance tube samples,
because this quantity depends only on the membrane and fluid mate-rial properties. The nondimensional characteristic impedance, however, is considerably larger for the noise shield MAMs, since Z0 is propor-tional to the MAM unit cell edge length, which is nearly three times larger than in the impedance tube measurements. Hence, from the pa-rameter study results shown in Fig. 2.24 it must be expected that the TL-peak bandwidth is strongly reduced for the larger MAM unit cells.
It follows that a suitable added mass configuration has to be found so that the noise reduction performance of the MAMs is notable in the measurements.
The parameter studies in Section 2.5 have identified which nondi-mensional MAM mass parameters are appropriate for tuning the MAM anti-resonance bandwidth. The eccentricity of a single mass as well as the mass radius of gyration have been shown to be inapplicable for the bandwidth control. Thus, the remaining tuning parameters of the noise shield MAMs are the nondimensional mass magnitudeµand the nondimensional mass diameter δM. According to the parameter study results in Section 2.5, these two parameters are used to control the MAM anti-resonance in the following way: First, the mass diameterδM
should be large in order to obtain a high anti-resonance bandwidth.
Secondly, since a higherδMshifts the anti-resonance to higher frequen-cies, the massµmust be increased accordingly. This, however, adds to the total mass of the MAM layers.
A parameter variation of these two mass parameters for the given MAM configurations revealed that it is difficult to find a suitable com-bination of δM and µ, when only one mass per unit cell is used. The chosen parameter combination has to ensure large anti-resonance band-widths at the desired frequencies and result in a mass geometry that is readily available on the market (due to the high number of masses required for assembly). However, this can be resolved by using two masses per unit cell with smaller diameters instead of one large mass.
Fig. 4.5(a) compares the analytically obtained transmission loss of a MAM element unit cell with one or two masses attached. In case of the single mass configuration, a cylindrical steel mass with DM = 50 mm and M = 11.6 g is attached to the center of the unit cell. The double mass configuration is illustrated in Fig. 4.5(b), where two masses with eachDM= 30 mm andM = 5.8 g are placed along they-symmetry axis with a spacing of Lx/3. The resulting static surface mass densities of both MAM configurations are equal withm00st= 820 g/m2. The analyt-ical results in Fig. 4.5(a) show that the transmission loss of both config-urations is nearly identical with a clear anti-resonance atfP1= 100 Hz.
In both cases, the anti-resonance bandwidth is equally good, except for an additional resonance and anti-resonance below 150 Hz for the dou-ble mass configuration, which occurs due to the additional mass. Since the MAM unit cell configuration with two masses yields smaller masses with larger thicknesses that are readily available on the market, this design is preferred over a single mass unit cell configuration for the MAM elements.
(b)Unit cell with two masses.
Figure 4.5: Sound transmission loss of a MAM element unit cell carrying one or two masses with the same total mass.
As shown in Fig. 4.5(a), the choice of two cylindrical steel masses with DM= 30 mm and M = 5.8 g yields an anti-resonance atfP1 = 100 Hz with a +10 dB-bandwidth (compared to the mass-law) of 36 Hz. There-fore, this design is chosen for the MAM unit cells on the first side of the MAM elements. In order to achieve an anti-resonance at a slightly higher frequency, smaller steel masses withDM= 20 mm and M = 2.6 g are selected for the other side of the MAM elements. This results in an anti-resonance at fP1 = 120 Hz and a slightly smaller bandwidth of 32 Hz. Table 4.2 summarizes the resulting nondimen-sional parameters for these two MAM configurations, with NS1 and NS2 corresponding to the MAMs with Ø30 masses and Ø20 mm-masses, respectively. With the given air gap between the two MAM layers as prescribed by the height of the MAM element grids (20 mm, see Fig. 4.4), the transfer matrix model is employed to estimate the normal incidence sound transmission loss of these MAM elements. The results are shown in Fig. 4.6(a). For comparison, Fig. 4.6(a) also shows the calculated sound transmission loss curves for the two individual MAM layers NS1 and NS2 (orange and purple dashed curves, respec-tively), as given in Table 4.2, as well as the corresponding mass-law curves (dash-dotted lines) with taking into account the mass of the grid (m00st = 5.6 kg/m2) and without the grid (m00st = 0.9 kg/m2). The
Table 4.2:Nondimensional parameters of the two MAM layers on each side of the noise shield MAM elements with two cylindrical masses per unit cell, as shown in Fig. 4.5(b).
Membrane Cylindrical mass (x2) Fluid
Conf. Λ Ξ ηm δM µ ϑ ξ∗ η∗ Z0 ς0
NS1 1.17 1.5×10−6 10−3 0.22 3.4 3×10−3 13; 23 0.5 12.9 7.4 NS2 1.17 1.5×10−6 10−3 0.15 1.5 1.3×10−3 13; 23 0.5 12.9 7.4
0 10 20 30 40 50
50 100 10001600
0.13 1 4
without grid with
grid
TLindB
fin Hz κ0
Mass-law MAM (NS2) MAM (NS1) MAM element
(a)Estimated transmission loss. (b) Photograph of a MAM element.
Figure 4.6:Analytically estimated normal incidence sound transmission loss of the MAM elements for the noise shield.
analytical results for the MAM element in Fig. 4.6(a) exhibit the well-known characteristics of stacked membrane-type acoustic metamateri-als [66]. The anti-resonances of each MAM layer are retained in this arrangement and an additional resonance occurs between the two ma-jor anti-resonances. As indicated in the top axis of Fig. 4.6(a), the nondimensional wave number κ0 is well below unity at the two anti-resonances so that the effective surface mass density approximation is valid in this frequency range. The combined bandwidth of the MAM element anti-resonances is determined to be 55 Hz, if the grid mass is not considered, and 11 Hz, if m00st = 5.6 kg/m2 is chosen as the refer-ence mass for the bandwidth calculation. This indicates that the grid mass has a strong influence on the resulting bandwidth of the MAM ele-ments. Therefore, the support grids for MAMs should be as lightweight as possible to minimize the amount of acoustical deadweight introduced into the structure.
Based upon these analytical predictions, the selected mass config-urations for the two layers of the MAM elements can be considered
as sufficient for meeting the requirements of the noise shield demon-strator. Therefore, all 25 MAM elements are manufactured according to this specification. Fig. 4.6(b) shows a photograph of an assembled MAM element with the nine unit cells containing the Ø30 mm-masses facing upwards.