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

Active poro-elastic acoustic meta materials
Christopher Robert FULLER 1
Vibration and Acoustics Laboratories, Virginia Tech, Blacksburg, VA, USA

ABSTRACTPrevious work has demonstrated the potential of poro-elastic acoustic meta materials for providing increased
sound absorption at low frequencies. This class of acoustic meta materials consist of a foam poro-elastic
matrix supporting periodic arrays of small spherical masses or microporous sheets. The increase in soundabsorption and/or transmission loss occurs either by the resonant dynamic motion of the embedded masses
or by resonant wave scattering between the microporous sheets. In this paper we report preliminary work on
extending the poro-elastic meta material to include active elements. The intention is to increase the bandwidthof the AMM attenuation which, due to it being based upon resonance conditions, is usually narrow. In theactive poro-elastic meta material some of the embedded masses are replaced with small inertial active
vibrators with the same weight and similar shape to the static masses. The control approach was a standard
digital feedforward approach. Tests were carried out with narrowband and broadband plane wave signals ina standing wave tube. The results indicate there is potential in using active elements to broaden the frequency
response of poro-elastic acoustic meta materials.
Keywords: Meta-material, active, poro-elastic

1. INTRODUCTION
There is a need to develop materials which have improved sound absorption with negligible mass
increase, particularly at low frequencies. In addition, the availability of designable passive damping
materials would be useful to the noise control engineer. Past work has demonstrated the potential of
poro-elastic acoustic meta materials(AMM) to address these needs(1,2,3). These class of AMM
generally consist of a poro-elastic matrix(foam fiberglass etc) containing embedded small sphericalmasses or thin, polymer microporous sheets. The embedded elements are often positioned in a periodic
manner, in the general arrangement of meta materials, although this is not always necessary. Figure 1
shows a poro-elastic AMM consisting of periodically arranged steel spheres embedded in melamine
foam. The left hand schematic shows the physical arrangement of the spheres embedded in a periodic
arrangement inside the foam. The right hand picture is a section through a constructed HG material
showing the spherical masses at one depth. In the finished HG material there is multiple layers offoam and masses stacked on top of each other. Other inserts such as plastic and hollow aluminum
spheres were studied along with different poro-elastic matrices such as polyimide and fiberglass.
The normal incidence absorption coefficients and transmission losses of different free standing
poro-elastic AMM samples were measured in a standard standing wave tube/TL test facility using two
and four microphones respectively in conjunction with cross spectral techniques to extract theparameters. In this test, a 4in sample of polyimide foam was embedded with 36 periodic 7/16indiameter spheres of polypropylene and steel with densities 927.8 kg/m3 and 7850 kg/m3, respectively.
The test results were also compared to COMSOL FEM predictions of the AMM material. Some
example results are given in the Figure 2 below. As can be seen in Figure 2, the numerical results
agree well with the experimental results using the different embedded masses. For the absorption
coefficient, the embedded masses/spheres can be seen to significantly increase the absorption
coefficient of the standard polyimide foam in the low frequency range near 200Hz. The transmission
loss measurements also show a significant increase in the low frequencies near 250 to 500Hz for bothsteel and polypropylene masses/spheres.
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cfuller@vt.edu

Figure 1. Arrangement of a typical poro-elastic AMM material; (a) schematic (b) section of aconstructed AMM material.

Figure 2. Measured and computed (a) absorption coefficients and (b) transmission losses ofvarious free standing poro-elastic AMM materials.

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While the results show much promise, they are limited to relatively narrow band behavior due tothe controlling resonant dynamics of the AMM system. The AMM effect is either due to resonant wave
scattering from spatially fixed elements or the dynamic resonance of the embedded elements. Thisnarrow band characteristics limits the applicable frequency range (and potentially angle of incidenceof impinging acoustic waves) of the AMM. In this paper, we summarize preliminary work in which
active inputs were used in an attempt to broaden the increased absorption/transmission loss range ofthe AMM.

2. ACTIVE PORO-ELASTIC ACOUSTIC META MATERIALS
2.1 Active AMM arrangement
To create an active AMM we replaced two of the static masses with very small inertial actuators
as shown in Figure 3. The active masses consist of a small plastic tube containing a circular magnet.
Coils of wire were wound around the outside of the tube to create a linear inertial vibrator. The active
mass can be seen to be of similar size and at 6gms, their mass was also very close to that of theembedded static masses.

Figure 3. Cross section of a polyimide based AMM with 10 polypropylene masses and two active
masses and (b) close up of an active mass.
The active AMM was positioned in a standard standing wave/transmission loss test tube as shown
schematically in Figure 4. The control system used was a digital feedforward system utilizing anupstream reference microphone sensor to pick up the sound and downstream error microphone
sensor(4). Since the control signal will appear on the reference signal, a feedback removal scheme
was used in the reference loop(4). Both narrowband and broadband noise signals were played throughthe primary sound source speaker.

Figure 4. Schematic arrangement of active AMM positioned in a standing wave tube and digital
active control system.

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2.2 Results
For the first tests, we consider narrow band noise excitation at tonal frequencies of 130 and 250Hz.
Note that for tonal noise, causality of the active system does not have an effect on control attenuation.
For the second set of tests, we utilize a white noise excitation band limited to 400Hz. In this latter
case, delay and hence causality through the control path is important in terms of performance. Figure
5 presents example test results. The narrowband results demonstrate that the use of active elements in
the AMM enhance the transmission loss/noise reduction by close to 20dB. The broadband results showthat the active elements provide increased noise attenuation over a bandwidth of 50 to 110Hz.

Figure 5. Performance of the active AMM (a) 130Hz noise signal (b) 250Hz noise signal and (c)white noise signal.

2.3

Active poro-elastic AMM for controlling vibration
In other related work active poro-elastic AMM was used to control the vibration of a cantileverbeam(5), repeated here as it directly relates to this paper. Figure 6 shows a schematic arrangement of
the test set up.

PZT
actuator

beam

foam

Massive base

Activemasses

accelerometer

Figure 6. Schematic of test set up used to investigate active AMM for controlling vibration.

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In the test set up a four inch layer of Melamine foam was glued to the surface of a 3mm thickAluminum cantilevered beam. The beam was driven into motion by a piezo-ceramic actuator(PZT)
located near the root of the beam. Five 6gm inertial masses were embedded in the foam as shown in
Figure 6 and an array of six accelerometers were positioned on the bottom of the beam to provide a
global estimate of the beam energy of vibration. A digital feedforward active control system was usedto drive the inertial active actuators and minimize the vibration at the five of the six accelerometers.
The reference signal was taken from the electronic disturbance signal to the PZT disturbance actuator.
The noise drive signal was appropriately delayed after the reference signal to cause the control system
to be causal. Figure 7 shows a photograph of the test set up.

Figure 7. Test set for active AMM control of beam vibration.
Figure 8 presents an example result. The solid black curve is the bare beam and can be seen tohave a number of peaks in the energy of vibration at the beam resonant frequencies. Addition of theplain Melamine foam to the beam can be seen to provide some attenuation of vibration at theresonances due to damping but little attenuation of vibration away from resonance as is normal passive
damping behavior. Addition of the active masses with control off and thus creation of a poro-elastic
AMM can be seen to provide significant additional passive attenuation at the low frequency peak near
150Hz and also broadband attenuation from 70 to 125Hz. This behavior, as shown in previouswork(1,2) , is due to the resonances of the embedded masses (inertial actuators) being in the range of
50 to 150Hz depending upon the depth to which they are embedded. When the active control system
is turned on, the active AMM can be seen to provide high attenuation of broadband beam vibration
over a range of 75 to 500Hz both on and off resonance. A global attenuation of beam vibration also
generally implies an attenuation of the coupler radiated sound although this is somewhat dependent
upon the radiation efficiency of the different structural mode shapes.

2.4 Discussion on status of active poro-elastic AMM
While the above work has demonstrated the potential of active AMM to enhance the frequency range
over which they can be applied, this is preliminary work and there are many questions remaining. For
the work on use of active AMM to directly reduce sound, the results are for normal incidence sound.
How the active AMM performs under oblique and random incidence sound needs to be studied.
Another important question concerns the actual physics of the active inputs to the AMM system; arethe active inputs directly modifying the impedance distribution through the poro-elastic material andthus its absorption/transmission of sound. In addition suitable wave deconvolving sensors within theporo-elastic active AMM need to be developed in order to make the material realizable.

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Figure 8. Results for active AMM control of beam vibration.

3. CONCLUSIONSThe preliminary work presented here has demonstrated the potential of using active inputs tobroaden the frequency of application of poro-elastic acoustic meta materials for controlling sound andvibration. However this was a preliminary investigation and may questions relative to the practicaldevelopment and use of such a material remain.

ACKNOWLEDGEMENTS
Some of the results of this paper were carried out with Adam Slagle as part of his M.S thesis at
Virginia Tech. Funding for this work by NASA Langley Research Center is gratefully acknowledged.

REFERENCES
1. Fuller, C.R and Saux, T.D, Sound absorption using poro-elastic acoustic meta materials, Proc. of Inter
Noise 2012, New York, NY, 2012.
2. Fuller, C.R and Mathur, G.P., Poro-acoustic meta materials, Proc. of Inter Noise 2017, Hong Kong, 2017.
3. Slagle, A, Low frequency noise reduction using poro-elastic acoustic meta materials and microperforated
panels, M.S Thesis, Virginia Tech, Blacksburg, VA, 2014.
4. Fuller, C.R, Elliot, S.E., Active control of vibration, Academic Press, London, 1996.
5. Fuller, C.R, Kidner, M.R.F, Li, X and Hansen, C.H., Active-passive heterogeneous blankets for controlof vibration and sound radiation. Proc. of Active 2004, Williamsburg, VA, 2004.

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