Noise shielding using active acoustic metamaterials ...

TECHNICAL UNIVERSITY OF LIBEREC Faculty of Mechatronics, Informatics and Interdisciplinary Studies

Noise transmission through active acoustic metamaterials in the negative elasticity regime Pavel MOKRÝ, Jan VÁCLAVÍK, Jakub NEČÁSEK Technical University of Liberec, Czech Republic

Pavel PSOTA, Roman DOLEČEK, Kateřina STEIGER Regional Center for Special Optics and Optoelectronic Systems TOPTEC, Czech Republic

TECHNICAL UNIVERSITY OF LIBEREC

Motivation • We are interested in a simple question: • Is it possible to efficiently suppress noise transmission through large glass structures without the use of microphones and loudspeakers?

Jul 13, 2015

ICSV-22, Florence

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Motivation  Noise shielding system based on active

acoustic metamaterials with electronically tunable acoustic impedance

• How does it work?

Jul 13, 2015

ICSV-22, Florence

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Noise shielding device • Principle of the noise transmission through planar structures

• Acoustic transmission loss and specific acoustic impedance at the interface 𝑝𝑖 𝑍𝑤 𝑇𝐿 = 20 log = 20 log 1 + 𝑝𝑡 2𝑍𝑎 Jul 13, 2015

ICSV-22, Florence

𝑝𝑖 + 𝑝𝑟 − 𝑝𝑡 𝑍𝑤 = 𝑣 4


Noise shielding device • Principle of the noise transmission through planar structures

• Acoustic transmission loss and specific acoustic impedance at the interface 𝑝𝑖 𝑍𝑤 𝑇𝐿 = 20 log = 20 log 1 + 𝑝𝑡 2𝑍𝑎 Jul 13, 2015

ICSV-22, Florence

𝑝𝑖 + 𝑝𝑟 − 𝑝𝑡 𝑍𝑤 = 𝑣 5


Noise shielding device • Reduction of the glass plate normal vibration

𝑍𝑤 Jul 13, 2015

𝑖ℎ 𝜔 ∝ 𝜚𝜔2 − 𝜁𝐺 𝜔 ICSV-22, Florence

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Noise shielding device • Reduction of the glass plate normal vibration 𝜉… curvature

~1/𝜉

1. Bulging the glass plate to make a curved shell 𝑍𝑤 Jul 13, 2015

𝑖ℎ 𝜔 ∝ 𝜚𝜔2 − 𝜉𝑌 + 𝜁𝐺 𝜔 ICSV-22, Florence

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Noise shielding device • Reduction of the glass plate normal vibration 𝜉… curvature

 How can we ~1/𝜉

increase Young’s modulus 𝑌?

1. Bulging the glass plate to make a curved shell 𝑍𝑤 Jul 13, 2015

𝑖ℎ 𝜔 ∝ 𝜚𝜔2 − 𝜉𝑌 + 𝜁𝐺 𝜔 ICSV-22, Florence

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Noise shielding device • Reduction of the glass plate normal vibration NC

Piezoelectric actuator

1. Bulging the glass plate to make a curved shell 2. Piezoelectric actuators shunted by a negative capacitor to increase Young’s modulus 𝑌 Jul 13, 2015

ICSV-22, Florence

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Noise shielding device Piezoelectric MFC actuator

Curved glass shell Rigid steel frame

Negative capacitor Jul 13, 2015

ICSV-22, Florence

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Noise shielding device MFC piezoelectric actuator Glass shell

Jul 13, 2015

ICSV-22, Florence

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Active elasticity control

 Effective spring constant of piezoelectric actuator can

be controlled by shunt circuit capacitance Y

𝑌 = 𝑌0

1 + 𝐶 𝐶𝑠 1 − 𝑘 2 + 𝐶 𝐶𝑠

Cs

C

Shunt circuit

𝑘…electromechanical coupling factor Jul 13, 2015

ICSV-22, Florence

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Active elasticity control 10

k=0.7

K /K0 𝑌/𝑌 0

5 0 -5

softening hardening

-10 -1.0

𝑌 = 𝑌0 Jul 13, 2015

1 + 𝐶 𝐶𝑠 1 − 𝑘 2 + 𝐶 𝐶𝑠

-0.5

C/Cs

𝐶/𝐶𝑠 → −1 ⇒ 𝑌 → 0 𝐶/𝐶𝑠 → −1 + 𝑘 2 ⇒ 𝑌 → ∞ ICSV-22, Florence

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k=0.7

K /K0 𝑌/𝑌 0

5

softening Negative stiffness

0 hardening

-5

softening hardening

-10 -1.0

𝑌 = 𝑌0 Jul 13, 2015

1 + 𝐶 𝐶𝑠 1 − 𝑘 2 + 𝐶 𝐶𝑠

-0.5

C/Cs

𝐶/𝐶𝑠 → −1 ⇒ 𝑌 → 0 𝐶/𝐶𝑠 → −1 + 𝑘 2 ⇒ 𝑌 → ∞ ICSV-22, Florence

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k=0.7

K /K0 𝑌/𝑌 0

5

softening Negative stiffness

0 hardening

-5

softening hardening

-10 -1.0

C/Cs

-0.5

 System may enter a regime with a negative effective stiffness  Noise shielding device = Active acoustic metamaterial? Jul 13, 2015

ICSV-22, Florence

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Tunable acoustic metamaterials

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ICSV-22, Florence

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Tunable acoustic metamaterials

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ICSV-22, Florence

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Measurement methods • In order to directly observe the elasticity mode of the noise shielding device, two real-time optical methods have been used:  

Jul 13, 2015

Laser Doppler vibrometry (LDV) Digital holographic interferometry (DHI)

ICSV-22, Florence

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Laser Doppler vibrometry

• Specific acoustic impedance: Jul 13, 2015

ICSV-22, Florence

𝑝𝐼𝑁 − 𝑝𝑂𝑈𝑇 𝑍𝑤 ≈ 𝑣 19


Digital holographic interferometry

Jul 13, 2015

ICSV-22, Florence

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Digital holographic interferometry 42 cm 30 cm

Jul 13, 2015

ICSV-22, Florence

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Digital holographic interferometry Laser beam

• Digital holography is based on the basic principle of interferometry • Two digital holograms are captured: – Reference static hologram – Hologram of vibrating shell

• Phase difference of optical fields is calculated • Bright stripes - points with the same displacement Jul 13, 2015

ICSV-22, Florence

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Glass shell vibrations

Jul 13, 2015

ICSV-22, Florence

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Suppression of noise transmission NEGATIVE CAPACITOR -C 0

-R 1

CS R2

MFC ACTUATOR

𝐶𝑠 = 2.07 𝜇𝐹 𝐶0 = −2.58 𝜇𝐹 𝑅1 = −116 Ω 𝑅2 = 575Ω

DIGITAL SYNTHETIC IMPEDANCE

NC ON

NC OFF

Jul 13, 2015

ICSV-22, Florence

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-R 1

CS R2

MFC ACTUATOR

𝐶𝑠 = 2.07 𝜇𝐹 𝐶0 = −2.58 𝜇𝐹 𝑅1 = −116 Ω 𝑅2 = 575Ω


NC ON

NC OFF

Jul 13, 2015

ICSV-22, Florence

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-R 1

CS R2

MFC ACTUATOR

𝐶𝑠 = 2.07 𝜇𝐹 𝐶0 = −3.173 𝜇𝐹 𝑅1 = −134.5 Ω 𝑅2 = 170 Ω


NC ON

NC OFF

Jul 13, 2015

ICSV-22, Florence

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-R 1

CS R2

MFC ACTUATOR

𝐶𝑠 = 2.07 𝜇𝐹 𝐶0 = −3.173 𝜇𝐹 𝑅1 = −134.5 Ω 𝑅2 = 170 Ω


NC ON

NC OFF

Jul 13, 2015

ICSV-22, Florence

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Suppression of noise transmission

Jul 13, 2015

ICSV-22, Florence

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Inverse specific acoustic impedance • Peak values of 𝑇𝐿 correspond large values of 𝑌 and 𝑍𝑤 𝑍𝑤

𝑖ℎ 𝜔 ∝ 𝜚𝜔2 − 𝜉𝑌 + 𝜁𝐺 𝜔

• At large values of 𝑌, the inverse specific acoustic impedance vanishes and changes the sign 1 𝑖𝜔 ∝ 𝑍𝑤 𝜔 ℎ𝑌

Measurement of 𝟏/𝒁𝒘 can be used to identify the negative elasticity regime of the device Jul 13, 2015

ICSV-22, Florence

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Inverse specific acoustic impedance • At large values of 𝑌, the inverse specific acoustic impedance vanishes and changes the 270 Hz sign 1 𝑖𝜔 𝑍𝑤 𝜔 𝑌 ′′ ∝ 1/𝑍𝑤 ′

Jul 13, 2015

∝

ℎ𝑌

𝑌 = 𝑌 ′ + 𝑖𝑌′′

ICSV-22, Florence

𝑌 ′ ∝ 1/𝑍𝑤 ′′

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Transmitted sound wave phase reversal • Negative value of Young’s modulus Phase of the transmitted sound wave is reversed

Jul 13, 2015

ICSV-22, Florence

270 Hz

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Inverse specific acoustic impedance • At large values of 𝑌, the inverse specific acoustic impedance vanishes and changes the 720 Hz sign 1 𝑖𝜔 𝑍𝑤 𝜔 𝑌 ′′ ∝ 1/𝑍𝑤 ′

Jul 13, 2015

∝

ℎ𝑌

𝑌 = 𝑌 ′ + 𝑖𝑌′′

ICSV-22, Florence

𝑌 ′ ∝ 1/𝑍𝑤 ′′

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Vibration displacement • Transition from ordinary to negative elasticity at 724 Hz

Jul 13, 2015

𝑌 ′′ ∝ 1/𝑍𝑤 ′

ICSV-22, Florence

𝑌 ′ ∝ 1/𝑍𝑤 ′′

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Jul 13, 2015

𝑌 ′′ ∝ 1/𝑍𝑤 ′

ICSV-22, Florence

𝑌 ′ ∝ 1/𝑍𝑤 ′′

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Jul 13, 2015

𝑌 ′′ ∝ 1/𝑍𝑤 ′

ICSV-22, Florence

𝑌 ′ ∝ 1/𝑍𝑤 ′′

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Jul 13, 2015

𝑌 ′′ ∝ 1/𝑍𝑤 ′

ICSV-22, Florence

𝑌 ′ ∝ 1/𝑍𝑤 ′′

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Jul 13, 2015

𝑌 ′′ ∝ 1/𝑍𝑤 ′

ICSV-22, Florence

𝑌 ′ ∝ 1/𝑍𝑤 ′′

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Transition to negative elasticity • Results of DHI measurements: • Color indicates the orientation (phase) of the displaced surface Displacement amplitude reversal indicates the transition to the negative elasticity regime

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ICSV-22, Florence

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Conclusions 1. Narrow frequency range noise shielding by 30dB at two resonant modes have been achieved 2. The specific acoustic impedance was directly measured using real-time optical methods 3. Transition from ordinary to negative elasticity has been observed

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ICSV-22, Florence

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The end… Thank you for your attention!

Acknowledgment: • •

Czech Science Foundation Project No.: GACR 13-10365S Ministry of Education, Youth and Sports of the Czech Republic in the Project No. NPU LO1206

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ICSV-22, Florence

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