PROCEEDINGS of the23rd International Congress on Acoustics
9 to 13 September 2019 in Aachen, Germany

Random Incidence Transmission Loss of Miniature Helmholtz
Resonator Embedded Acoustic Meta-material
Jhalu GORAIN1; Chandramouli PADMANABHAN21, 2

Indian Institute of Technology Madras, Chennai-600036, India

ABSTRACTAn array of light-weight miniature Helmholtz resonators (HRs), was shown to significantly enhance the low
frequency absorption, when embedded in a PU foam material; this test was carried out in an impedance tube.
This concept was then used to study the sound absorption in a cylindrical cavity. A series of tests were carriedout by changing number of HRs, embedded circumferentially into foam, at various radial distances on top of
the cavity, with a noise source at the bottom. About 8-14 dB reduction in noise levels was observed at lowerfrequencies. In this paper, the idea is now extended to examine the random incidence transmission loss (TL)of such an array of embedded HRs. Towards this purpose, a twin room reverberation chamber with a 300 mmx 300 mm panel in between is used; random incidence is carried out using first a 45 mm foam alone followedby the foam embedded with a periodic array of HRs. The effectiveness of this concept to increase TL at lower
frequencies will be demonstrated. Also, by adjusting the resonator frequencies, by intruding the neck into
resonator cavity, is shown to increase the TL over a broader range of frequencies.
Keywords: Miniature HR, Meta-material, Transmission Loss.

1. INTRODUCTION
Controlling low frequency noise is still a great challenge in industry and daily life. One of theearliest attempts to solve this problem was the development of a micro-perforated panel (MPP)
absorber (1, 2). Following this idea, the use of Helmholtz resonator (HR) (3) with many modifications
such as degenerate resonators (4), resonant patches (5) and multiple orifices (6) have been introduced.
These solutions have typically been effective in narrow frequency bands and in the case of HRs lead toincreased weight due to large dimensions of the HRs.
Another possible solution that has been suggested is to use porous material with mass inclusion (7).
The embedded masses combined with porous material form an array of spring -mass-damper system
and improve the acoustic performance. Later, this type of mass embedded material was named asheterogeneous blanket (HG). For further improvement in transmission loss and absorption capability,
the proposed HG blanket was investigated with various embedded mass such as steel balls, Styrofoam
balls and hollow aluminum balls (8). These again do not yield fairly broad band low frequency noise
reduction.
The third and latest set of solutions to mitigate a low frequency sound is the acoustic metamaterials(AMM). In an AMM a periodic arrangement of masses is being done at a scale smaller than thewavelength to be captured. The first AMM, sonic crystal (9) was demonstrated using lead balls
covered with silicone rubber. The author who proposed the HG blanket explored the tr ansmission loss
as well as absorption coefficient using mass embedded and MPP based AMMs (10, 11). At around thesame time, the effect of a resonant inclusion in a porous material was investigated using TMM andP-TMM based analytical modelling approach (12). Apart from the porous media based AMMhoneycomb based AMM (13), membrane and plate-type (14) AMMs have been developed and theireffectiveness demonstrated through experiments. But all of them are heavier because of either larger
thickness of porous media or larger dimensions of HR/included masses and perform only over alimited low frequency range. Further, most of the researchers have examined mostly the normal
incidence absorption coefficient and transmission losses characteristics of the developed materials.
This paper, after briefly summarizing the earlier work done by the authors on miniature HR based
acoustic meta-materials, will focus on the experimental investigation of random incidencetransmission loss (TL) of the miniature HR embedded AMM. The material is fabricated by embedding
1
2

gorain@smail.iitm.ac.inmouli@iitm.ac.in2083

an array of cylindrical cavity miniature HRs into PU foam and tested in twin reverberation chamber.
The relative transmission losses are reported here. Also the differences and advantages over otheracoustic metamaterials will be highlighted.

2. SUMMARY OF PRIOR WORK
2.1 Idea of Miniature HR embedded AMM
To reduce the size and to get an enhanced absorption capability over a broader frequency range, theidea of miniature HR is proposed by using syringes of different sizes. The dimensions and geometry
details of medical syringes for considered frequencies are given in the Table 1.
Table 1 – Different types of geometries of HR
Syringe

Geometry

CavityCavityNeck

CavityTargeted

Size

Type

DiameterHeightDiameterHeightFrequency

(mm)

(mm)

(mm)

(mm)

(Hz)

(cc)
10G1142429480

10G2145829350

10G31486

29265

A series of tests were conducted in a 6 inch impedance tube designed as per ISO standards at IITMadras. For the proof of concept of miniature HR, detuning of HR, and formation of new AMM a totalof four sets of experiments were carried out using the impedance tube. After confirming that the ideaof using syringes as HRs does work further investigation was done with a sample, made of 9 syringes(3 G1 type, 3 G2 type and 3 G3 type) with one placed at the center and 8 at the circumference of a platewith a radius of 55 mm. The determined absorption coefficient is shown in Figure 1.

Figure 1- Absorption coefficient of multiple HRs.
One can see that the overall absorption between the peaks are also improved in experiment; the 1D
analytical model has a model for radiation impedance included and hence the anti -nodal regions are
somewhat higher compared to the finite element model (done in COMSOL), where only a small
dissipation is added to the air medium and hence shows narrower peaks. The same set of experiments
were repeated with HRs embedded in a 20 mm PU foam as shown in Figure 2 (a). In Figure 2 (b) a2084

typical mass embedded 4 inch AMM is shown.

Figure 2- (a) 1 inch HR embedded AMM (b) 4 inch AMM (reproduced from reference 11)
The absorptive performance of 20 mm foam is quite low over the chosen band. At 26 5 Hz the
combined effect of foam and HR, shown in Figure 3, is similar to the previous case as shown in Figure
1, but at and beyond 350 Hz its effect is visible.

Figure 3- Absorption curve of HR embedded AMM
Also the anti-resonance deep between the peaks are also slightly lifted up which is good from anabsorption view point. And more importantly, below 500 Hz, the new metamaterial has shown agreater broad band absorption capability when compared with the idea s proposed in the literature. The
developed metamaterial is light in weight and cheaper in cost. So, newly designed HR embedded
acoustic metamaterial is very much suitable for payload fairings and car cabins.
2.2 Cavity Demonstration of the new HR embedded AMM
For checking the effectiveness of the proposed novel material in real life or equivalent problems ademonstration was conducted in a cylindrical cavity shown in Figure 4.

Figure 4. Schematic of cavity demonstration set up
A series of experiments were conducted with four different conditions, shown in Figure 5, as2085

follows: cavity with top acrylic plate only, acrylic plate with 20 mm PU foam of density 16 kg/m3 only,
acrylic plate with HRs only and, and acrylic plate with new AMM (Foam+ HR).

Figure 5- Acrylic plates in different test conditions
The typical dimensions of HRs for the first axial mode 262 Hz are the same as mentioned in theTable 1. For case 3 and 4, a total of 36 HRs are placed in the acrylic plate at three different radii asshown in Figure 5. The number of HRs placed at the periphery of circle of radius 8 cm, 16 cm and 24cm 8 are 8, 12 and 20 respectively.
The first set up was done with acrylic plate only and subsequently other three. For investigating
the effect of the HR embedded AMM over a range of 200-550 Hz, a combination of different
dimensions of HRs were placed at 3 different places. A combination of 18+18 HRs for targetingfrequencies 265 Hz and 532 Hz was used. The positions of HRs were interchanged and investigatedtheir effectiveness.
The red dotted line in Figure 6, shows 10 dB and 13 dB reduction in SPL at frequencies
265 Hz and 532 Hz respectively. It can be seen that around 265 Hz the noise reduction is entirely due
to the resonators while at 532 Hz the resonators enhance the absorption offered by the foam.

Figure 6- Reduction of SPL (dB) w.r.t. the cavity at different cases for 265 Hz and 532 Hz2086

3.

TRANSMISSION LOSS MEASUREMENT

3.1 Experimental Set Up
The transmission loss measurement for random incidence of sound is usually done in areverberation chamber. A reverberation chamber (RC) consists of two closed chambers. The soundsource is placed in the larger chamber and sample is fitted in the junction of two chambers. A
schematic diagram of twin reverberation chamber is shown in Figure 7.
ReceiverChamber
SourceChamber

Figure 7- Schematic of twin reverberation chamber
Two quarter inch condenser type microphones, one in the source chamber and another in thereceiver chamber, are placed to measure pressure level at various locations. Both the microphones areconnected with data acquisition system for storing and post processing the measured data in frequency
as well as time domains. The input which is a wide band sound in the source chamber is produced by
B & K sound source at a particular dB level.
3.2 Sample Preparation
The sample tested in the chamber is made of PU foam in which miniature HRs can be embedded.
Here instead of 20 mm a 45 mm PU of dimension 300 mm x 300 mm is used. It was done to make thesample leak-proof and fully embed HRs. The syringes which were used as HRs are now replaced by astandard cylindrical geometry as shown in Figure 8.

Figure 8. Equivalent miniature HR of syringes
For making the design of HR more compact the concept of intrusion of neck into to the cavity isalso implemented. The neck length is fixed at 2 mm from the top surface of the cavity. Basically only
two types of samples are investigated: one with only foam and other with HR embedded foam as shownin Figure 9 (a) and (b). The total number of HRs embedded are 36.

Figure 9- (a) 45mm PU foam only (b) HR embedded foam2087

All 36 HRs tuned to a single frequency (360 or 465 Hz) or 18 of them to 360 Hz and 18 to 465 Hz.
The change in the HR resonant frequency is accomplished by changing the intrusion length of theresonator neck into the cavity.
3.3 Results and Discussion
In the first phase of measurement, only PU foam is tested and transmission loss (TL) is evaluated.
Keeping all boundary conditions same, the same measurement is repeated with HR embedded AMM
tuned at 360 Hz. A point to note here is that in the calculation of the TL the term due to reverberation
time is excluded. Since it is a constant so the nature of the curve will not change. Therefore, in Figure
10, the relative TL is shown demonstrates a significant improvement around the HR natural frequency.

Figure 10- TL of HR embedded AMM relative to foam tuned at 360 Hz
It is interesting to note here that rather than a single sharp peak, one can see a spread around 360 Hz.
The 360 Hz is achieved from the baseline 465 Hz design by intruding the neck into the cavity. Since
this was done manually there are some small variations in the resonator frequency leading to bette r
performance over a wider band Figure 11 shows the results for the resonators tuned to 465 Hz and here
the peak is quite sharp as these form the baseline design.

Figure 11- TL of HR embedded AMM relative to foam tuned 465 Hz2088

One of the prime objectives of the paper to obtain a broad band AMM for low frequency noisecontrol. So, next an experiment is conducted targeting two frequencies. Out of 36 18 HR are tuned at360 Hz and other 18 are at 465 Hz. The relative TL is shown in Figure 12.

Figure 12- TL of HR embedded AMM relative to foam tuned at 360 Hz and 465 Hz
Again one can notice that there is a broader frequency range around the designed HR resonanceswhere the material performs well. The prime reason behind it is that the HRs are made by assembling
three parts (cavity, bottom cavity cap and neck) manually. This can lead to small detuning of theresonances and hence the broader range. This would suggest that detuning the resonators can be usedto widen the improved TL region for such materials.

4. CONCLUSIONSThe experimental investigation of the miniature HR embedded AMM shown a relative transmission
loss of 12-15 dB over a broader band of frequency in random incidence condition. Moreover, it is now
confirmed that using multiple resonators with intrusions for different frequency the acoustic
performance of AMM can be enhanced. And also the size of embedded HRs are smaller than proposed
AMMs in the literature. It indicates that the material has great potential in real life applications such asbuilding acoustics, car cabin, payload fairings etc. Future work will focus on the effect of the array
periodicity on the acoustic performance of such AMMs.

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