3J2-2
Design of Acoustic Meta-surfaces with Both Coincidence EffectSuppression and Sound Absorption Functions
Tomoya Ishikawa†, Masaaki Misawa, and Kenji Tsuruta*(1Grad. School Nat. Sci. & Technol., Okayama Univ.)

1. Introduction
The coincidence effect[1], an enhanced
transmission of incident sound through the wall,
occurs when the wavelength of the wall flexual(Lamb) wave and that of the incident sound wave
coincide with each other. This effect has to bealways considered in designing structuralcomponents of buildings, infrastructures, andautomobiles.
In this study, we focused on designing an
acoustic meta-surface[2-5] that is thinner than thewavelength of sound, but, exhibits the soundinsulation for wide range of frequency bysuppressing the coincidence effect without
additional sound absorbing materials or changing
the wall thickness. The two-dimensional finite
element method (FEM) was employed to search forthe optimum structure that exhibits the above
characteristics in the audible frequency range (1000
Hz to 3000 Hz).

acoustic meta-surface (Structure 1).

Figure 2 shows that in the case of the plate withperiodic hole array (“Structure 1”), the transmission
loss is kept at high dB in the frequency range where
the coincidence effect has occurred in the “Normalwall”. The inset of Fig. 2 also shows that thedisplacement in Structure 1 at the frequency is
extremely small compared to that in the normalwall. This can be attributed to the presence of gap
frequency where the Bragg scattering of the Lambwave is undertaken in the thin plate, thereby
blocking sound around the frequency at which thecoincidence effect occurs.

2. Acoustic Meta-Surface based on PeriodicStructure
To reduce the coincidence effect in thin plate,
we adopted to introduce a periodic array of hole in
the plate. Figure 1 illustrates the unit cell of theproposed structure. When a plane wave of 1 Pa isincident on a 26 mm thick aluminum wall withoutholes at an incident angle 30°, the transmission loss
drops significantly at 1938 Hz, as designated as“Normal wall” in Fig. 2. As illustrated in the insetof Fig. 2, the wall is greatly displaced in response tothis wave, indicating the occurrence of thecoincidence effect.

Fig.1 Cross section view of unit cell in the proposed*e-mail: tsuruta@okayama-u.ac.jp

Fig. 2 Transmission loss spectra and (inset)
displacement distributions in the “normal wall” and“Structure 1” at 1938 Hz.

In addition to the sound insulation by
suppressing the coincidence effect, we aimed anadditional function in the meta-surface byintroducing a neck at the top of the hole, as depicted
in Fig. 3. Figure 4 shows transmission loss
spectrum of the metasurface structure depicted inFig.3 (designated as “Structure 2”). The figure
indicates that Structure 2 not only prevents thecoincidence effect, but also shows a peak where thetransmission
loss
increased.
Severalsound-absorbing meta-surfaces have been proposed
recently, e.g. a sound-absorbing device called
Decorated Membrane Resonator (DMR)[3], which
induces enhanced vibration of a membrane via its
hybridized mode between membranes’ normalmodes and an air layer. Sound energy is converted
into thermal energy through the vibration of thematerial, resulting in the efficient sound absorption.
In the present model, the sound absorption is caused

by the vibration of the neck section. The vibrationof the wall is considerably reduced, and hence thetransmission becomes low, while the reflection isalso small at the frequency. This indicates highly
efficient energy conversion from sound to neckvibration occurs predominantly through themechanism described above at the frequency.

Fig. 3 Cross section view of unit cell in the
proposed acoustic metasurface with soundabsorption (Structure 2).

Fig. 4 Transmission loss spectrum for Structure 2and (inset) displacement distribution at the peakfrequency.

Conclusion
By using the FEM analysis, we havedesigned two types of acoustic meta-surface
structure with periodically arranged holes thatprevent the occurrence of the coincidence
effect as well as the sound absorption function.
As a result, the coincidence effect wasefficiently suppressed and a peak with aconsiderably higher transmission loss wasobtained due to the sound absorption effectgenerated by the resonant vibration of the neckin the structure. The proposed approach may
be used various structures where the highinsulation of sound is required within limited
space and weight.
Further designing of multiple absorption
peaks toward the wider band applications isbeing investigated. The actual fabrication andmeasurement of these proposed structures will
be performed and reported in the presentation.

Acknowledgement
This work was supported in part by the JSPS
KAKENHI Grant Numbers 21H05020 and21K18877.
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Composite Structures 200, 15 (2018) p. 165 –172
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