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

Development of a metamaterial for acoustic and architectonical improvement of window
design.

Gioia FUSARO1,2; Xiang YU1; Fangsen CUI1; Jian KANG3
1
2

Institute of High Performance Computing, A*Star, Singapore

School of Architecture, Acoustics Group, University of Sheffield, UK

3

UCL Institute for Environmental Design and Engineering, The Bartlett, University College London, UKABSTRACT
The development of windows which can address the issue of high noise levels while maintaining naturalventilation has drawn significant attention recently. However, there are limitations to traditionalGouble
glazing together with duct designs. Previously, window systems have been developed based on the local
resonant stopband of acoustic metamaterial (AMM) to achieve dual functions of noise reduction and naturalventilation. In this study, a new effort is made to develop a window system with foldable origami
metamaterial, which conceptually proposes a novel approach for acoustic and ventilation design. The
proposed device allows air exchange between the interior and exterior domains, and it forms anomni-directional acoustic metacage in the folded state. This paper elaborates the design concept of theproposed device and the important design parameters. The sound reduction performance is investigated using
Finite Elements Method (FEM) simulations. The numerical method developed in this work can facilitate theoptimisation of origami metamaterial for real window designs.
Keywords: Metamaterials, Ventilation, FEM.

1. INTRODUCTION
Conventional acoustic techniques allow controlling sound waves within a limited range offrequencies. Generally, noise control devices are bulky in order to operate in the typical airborne noisefrequencies (1–5). Acoustic metamaterials are very versatile owing to its excellent properties related
to its physical size (6,7). Particularly, origami metamaterial greatly extends the tuning ability anddesign range of existing metamaterial benefiting from its unique geometric flexibly. Recent studies
have shown that origami folding can be combined with appropriate acoustic and mechanical design toimprove the performance in many regards (8-10). Based on the interesting origami concept and theencouraging results so far, metamaterial window design with a specific aim to achieve both noise
reduction and ventilation can be further improved.
This study presents the conceptual design of a novel origami acoustic metacage, whoseperformances are tunable during the reconfigurable process. The working principle for noise reduction
is similar to the acoustic metacage structure proposed earlier (11), while the origami enables a uniquemechanism to effectively vary the acoustic and ventilation characteristics in the folded and unfolded
state. Starting from the metacage concept, a design to allow expansion and compression of circularboundary surrounding a sound source is developed as illustrated in Fig. 1. Unique structural design on
the boundary forms a couple of metamaterial units in the folded state, which can control sound wave
radiation to the exterior domain through the ventilation apertures. Two types of ventilation conditions
are considered in this study, according to Fig. 1. Design 1 has distributed perforations along theperimeter, while Design 2 has ventilation apertures and thus much larger ventilation volume . In thefirst case, the open ratio (open surface/total perimeter) is 32% while for the apertures one is 52%. The
folded and unfolded configurations of the two designs are compared in Fig. 1. As a preliminary study,
only the two extreme configurations (completely folded and unfolded) are tested using 2D Finite
1

gfusaro1@sheffield.ac.uk (G Fusaro)
cuifs@ihpc.a-star.edu.sg (F Cui)3
j.kang@ucl.ac.uk (J Kang)
2

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Elements Method (FEM) simulations, hopefully, to demonstrate the dramatic change in the acoustic
property resulted from the origami metamaterial.

a1

b1

a2

b2

Figure 1– Schematic of Design 1 (Origami metacage with perforations) (a1) and Design 2 (Origami

metacage with apertures) (b1) in the folded and unfolded (a2,b2) state. The yellow and light blue dots
denote the movements of the folding points along the boundary: valley folds (light blue), and mountainfolds (yellow).
This paper aims to demonstrate the effectiveness of this novel metamaterial for window
applications. This model can be used at different frequency ranges (100-10000Hz), and several
dimensions (0.2, 1, and 2 m in diameter) are tested to show the shift of working frequency with respect
to system size. The device can be incorporated into a window without obstructing natural lighting fromthe outdoor environment. An inversely proportional correlation between the shifting of th e mostaffected frequency range and the model dimensions is expected. This phenomenon should beaccompanied by a Sound Pressure Level (SPL) dip, according to the resonator nature of thismetamaterial.

2. METHODOLOGY
2.1 Geometrical Setting
In this research, the acoustic wave propagation is set to be originated from the interior of theorigami metacage and radiates out through the distributed ventilation holes along the surface . The
actual 3D system can be viewed as a protrusion from the 2D plane, where each cross-section has thesame geometry. For this reason, 2D simulation is carried out for the sake of computation efficiency.
The 2D FEM model represents the geometry of the origami metacage, and the folded and unfolded
configurations are illustrated in Figure 2. The diameter of the metacage (refer to unfolded state) is 0.2
m and 0.4 m for the circular outer boundary. This diameter ratio 1:2 is kept the same for all thesimulation cases with different scales which will be tested later, in order to understand the effect of1978system size on the frequency range.

Figure 2 – Geometrical configurations of Design 1 (folded and unfolded) and boundary conditions: central
point source, interior sound hard boundaries (blue), and cylindrical free wave radiation (dashed line).
The folded configurations represent in 2D an octagonal star (eight points) with 0.05 m length ofeach side. In each of these extremities two cavities are positioned towards the cent re of the triangularpoint, delimited by layers which start from the sides and extend towards the mid dle of it for
respectively 0.008 m, 0.012 m, and 0.016 m, and cavities width as 0.008 m (see Figure 2). A parametricstudy, done to see an acoustic effectiveness difference while changing those components dimension,
supports the setting of the dimension of both cavities and central duct (see Figure 3). The parametricstudy took in consideration three width configurations for the cavities (a= 0.007, 0.008, 0.009 m) andthree for the central duct (b=0.007, 0.008, 0.009 m). From the results, it is clear that the cavities widthchange does not affect the metacage performance, so for the next parametric study, the a 2 configuration
will be used. The next results show that the central duct width change does not affect the metacage
performance in the considered terms of dimension changing. So the configuration a 2 and b2 can be set
as standard as explained before. The acoustic and airwave propagation from the inside to the outside of
the metacage and vice versa is guaranteed by the resulted duct of width 0.008 m and by the four holesof 0.008 m length each on the point. When the geometric configuration passes from the folded to theunfolded one (see Figure 2), the sides of each extremity open and generate a circular perimeter shape.
The holes rotate with the sides, and the layers that constitute the cavities rotate as well until gettingoriented towards the centre with displacement from the direction perpendicular to it of 30° (see Figure2).

Figure 3 – Dimensions of the metamaterial unit formed in the folded state for Design 1.

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2.2 Boundary Conditions and Study Settings
The numerical model is implemented using commercial FEM software Comsol Multiphysics underAcoustics module. A monopole point source is placed at the centre of the origami metacage with avolume flow rate of 0.01 m2 /s. At the outer boundary, cylindrical wave radiation is defined to simulate
free outgoing waves without reflection. The simulation domain is filled with air, where air density andsound speed at room temperature are used. The walls of the metacage and material cells are set asinterior sound hard boundaries, as depicted in Figure 2. Sound transmission through walls of themetacage and possible viscous-thermal effect in the narrow resonator channels are neglected in thisstudy.
The SPL is averaged at the outlet boundary (dashed line in Fig. 2), to compare the acoustic responsein the unfolded and folded state. A decrease in the SPL curve will thus indicate less efficient soundradiation because sound energy is more confined in the metacage. The mesh size is determinedaccording to the FEM criterion, where at least six nodes are used to simulate a wavelength in air. To
reach 10000 Hz, the maximum allowed element size is thus 343/6/10000= 0.0057 m. The study is afrequency domain analysis from 100 Hz to 10000 Hz with a step size of 100 Hz. In the results, the SPL
radiation is shown linearly in the simulation frequencies.

3. NUMERICAL RESULTS
3.1 Design 1
Figure 4 first shows the simulation results of Design 1 in the folded and unfolded state. The
averaged SPL at the radiation boundary is between 40 dB and 120 dB, where some variations and peaks
can be observed due to the resonance of the circular enclosure. From the SPL radiation graph (Figure4a), both the folded and unfolded configuration effects are analysed. For the folded one the SPL
radiations reduce significantly at low frequencies (average of 106.6 dB of SPL), while in medium
frequency it loose efficacy, and from 2500 Hz to go on, an increasing sinusoidal behaviour starts, witha SPL average of 90 dB and a SPL dip of 48.7 dB at 8100 Hz. Figure 4b and 4c highlight theconfinement effect of the SPL at the different dip frequencies for both unfolded (dip at 4700Hz) andfolded (dip at 8100 Hz) configurations. In both graphs, it is evident how the folded state has a higher
acoustic impact on the sound wave confinement.
abc

Figure 4 – SPL radiation (a) and SPL distribution graph for 0.2 m Design 1 at 4700 Hz of the unfolded (b)and 8100Hz of the folded configuration (c).

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3.2 Design 2 and Comparison with Design 1
In the next subsection, the results of Design 2 are analysed and compared with Design 1. From thegraph (Figure 5a and Figure 6) it is evident that the acoustic behaviours of the two samples are thesame. This conclusion is visually supported also by the SPL distribution graph (Figure 5b and 5c),which shows how the distribution of the colour is similar. Moreover, also for Design 2, both graphs
show clearly how the folded state confine the sound wave in the internal part with more effectiveness.
This comparison result (between Design 1 and Design 2) is significant to understand how the design
can allow a better ventilation condition without affecting the acoustic performance of the device. This
improvement, as explained in the introduction about purposes, is needed to have proper ventilation of
the contained mechanical or of the physical system.
abcFigure 5 – SPL radiation (a) and SPL distribution graph for 0.2 m Design 2 at 4700 Hz of the unfolded (b)and 8100Hz of the folded configuration (c).

Figure 6 – Comparison between SPL radiation of Design 1 and Design 2.

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3.3 Comparison of the Different Scaled Models
This section focuses on the correlation between the dimension of the device and the SPL reduction
effect of it. For the sake of completeness, bigger samples of both Design 1 and Design 2, are built andanalysed through the same acoustic simulation settings. Although, since the behaviour of Design 1 andDesign 2 is mostly identical, it can be reasonable to consider using the second one to improve theventilation for the same reason explained before. So for the sake of simplicity only results related toDesign 2 will be presented, comparing the performance of the original model with those of diameter
equal to 1 and 2 m.
From the results, it is clear that, as expected, the increasing of the dimensions (five and ten times
bigger in this case), causes a shift of the SPL reduction peak towards lower frequencies. In particular,for the folded configuration, in the 1 m model, the dip is at 1600 Hz (Figure 7) with SPL of 38.25 dB.
This phenomenon happens consistently and progressively with the increasing of the models, and it isdemonstrated by the other study with dimensions ten times bigger than the original ones. For the 2 mmodels, the dip is at 800 Hz where SPL is 31.95 dB.
From Figure 7, the effectiveness of the origami metacage it’s demonstrated in this frequency range,
and the contribution of the folded configuration in this process is proved.

Figure 7 – SPL radiation of Design 2 with 0.2, 1, 2 m diameter.

4. DISCUSSION ON POSSIBLE DESIGN APPLICATIONS
The main aims of this research are achieved, and further experimental study will give more
completeness to the research. So now new possibilities are open for devices’ design which aim noise
reduction together with natural ventilation. Applications can interest both private and public spaces,
which are affected acoustically from the co-existence of different activities or infrastructures. For
these reasons, windows systems might be taken into account. The proposed geometry may beembedded in a window design built on an external wall of a private or public building such as a house,a school or a hospital. The resulting SPL broad dips of 38.25 dB and 31.95 (1 and 2 m diameter model)
might result of some impact in a situation where the area surrounding these buildings is very crowded,or when there are overlapping activities which might create high-level noise. An example could be toembed a system of origami metacage ducts in window frames or using the structure itself withincreased width and a transparent back panel to allow also light exchange between two environments.
A validation work will follow to test the actual building feasibility of a prototype and determine
whether if the transparent back panel might affect its performance or allow a new generation of tunablewindow systems.

5. CONCLUSIONSThis study has investigated the acoustic characteristics of a proposed origami acoustic metacage
with a unique reconfigurable mechanism. Two configurations with different ventilation designs(perforations/apertures) have been tested to assess the noise reduction and estimate the ventilation

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volume between the inside and the outside of the origami metacage (from 32% to 52% of openingratio). The folded metacage shows a profound dip in the radiated SPL due to the excellent silencing
effect provided by the metamaterial unit in front of the ventilation holes. The frequency a nd bandwidthof the effective region are related to the geometric parameters and scales of the system. 1atural air
ventilation is possible without any additional element, showing the potential of the proposed device tobe used in ventilation window systems. The developed numerical model can be further employed to
optimise the size and shape of the device to achieve better ventilation and noise reduction in thedesired frequency range.

ACKNOWLEDGEMENTS
The first author, Gioia Fusaro, acknowledges A*STAR (Agency for Science, Technology andResearch) and the University of Sheffield for the PhD scholarship used to finance her research.

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