# Optimization of Ultrasonic Acoustic Standing Wave Systems

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## Abstract

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## 1. Introduction

## 2. Model Setup

## 3. Model Based Optimization

## 4. Nonlinear Effects

## 5. Experimental Validation

## 6. Conclusions and Outlook

## Author Contributions

## Acknowledgments

## Conflicts of Interest

## References

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**Figure 3.**Sound field pattern between transducer and a plain reflector at distances of $L=17$ mm (

**a**) and $L=66.4$ mm (

**b**); maximum pressure level points marked with x; $f=21.4$ kHz; $\widehat{x}=19$ $\mathsf{\mu}$m.

**Figure 4.**Maximum sound pressure level (SPL) from FE-Model over varying distance between transducer and plain reflector; $f=21.4$ kHz; $\widehat{x}=19$ $\mathsf{\mu}$m.

**Figure 6.**Sound pressure level (SPL) from FE-Model over distance L for concave ($R=72$ mm) and plain reflector; $f=21.4$ kHz; $\widehat{x}=19$ $\mathsf{\mu}$m.

**Figure 7.**Sound field pattern between transducer and a concave reflector ($R=72$ mm) at distances of ${L}_{1}=17.4$ mm (

**a**) and ${L}_{2}=67.8$ mm (

**b**); maximum pressure level points marked with x; $f=21.4$ kHz; $\widehat{x}=19$ $\mathsf{\mu}$m.

**Figure 8.**Sound pressure level (SPL) from FE-Model over distance L for concave reflector on both sides and plain reflector; $R=72$ mm; $f=21.4$ kHz; $\widehat{x}=19$ $\mathsf{\mu}$m.

**Figure 9.**Sound field pattern of a system with concave reflector on both sides (both $R=72$ mm) at a resonant distance of $L=117.5$ mm (

**a**) and for a system with single concave reflector ($R=72$ mm) at a resonant distance of $L=118$ mm (

**b**); maximum pressure level points marked with x; $f=21.4$ kHz; $\widehat{x}=19$ $\mathsf{\mu}$m.

**Figure 10.**Sound pressure (microphone measurement) on a single point with sound pressure levels of ${L}_{p}=139$ dB and ${L}_{p}=166$ dB.

**Figure 11.**Experimental setup of the ultrasonic standing wave system with concave reflector and microphone.

**Figure 12.**Comparison of simulated and measured field patterns for standing wave system with plain reflector at a distance of $L=4\lambda $; sound pressure (model) and virtual velocity (experiment) are scaled logarithmically; $f=21.4$ kHz; $\widehat{x}=19$ $\mathsf{\mu}$m.

**Figure 13.**Comparison of simulated and measured field patterns for standing wave system with concave reflector ($R=72$ mm) at a distance of $L=4\lambda $; sound pressure (model) and virtual velocity (experiment) are scaled logarithmically; $f=21.4$ kHz; $\widehat{x}=19$ $\mathsf{\mu}$m.

**Figure 14.**Comparison of simulated and measured field patterns for standing wave system with concave reflector on both sides ($R=72$ mm) at a distance of $L=7.5\lambda $; sound pressure (model) and virtual velocity (experiment) are scaled logarithmically; $f=21.4$ kHz; $\widehat{x}=19$ $\mathsf{\mu}$m.

**Figure 15.**Sound pressure (measured with microphone) versus virtual velocity (measured with laser vibrometer).

**Figure 16.**Sound field pattern of standing wave system with concave reflector at distance $L=4\lambda $; left colorbar shows measurement of virtual velocity ${v}_{rms}$; right colorbar shows sound pressure level ${L}_{p}$ after scaling; $f=21.4$ kHz; $\widehat{x}=19$ $\mathsf{\mu}$m.

**Figure 17.**Sound pressure level (SPL) along the rotational axis of a standing wave system with concave reflector at a distance of $L=4\lambda $; $f=21.4$ kHz; $\widehat{x}=19$ $\mathsf{\mu}$m.

**Figure 18.**Sound pressure level (SPL) along the rotational axis of a standing wave system with concave reflector at a distance of $L=4\lambda $; $f=21.4$ kHz; $\widehat{x}=2$ $\mathsf{\mu}$m.

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**MDPI and ACS Style**

Dunst, P.; Hemsel, T.; Bornmann, P.; Littmann, W.; Sextro, W. Optimization of Ultrasonic Acoustic Standing Wave Systems. *Actuators* **2020**, *9*, 9.
https://doi.org/10.3390/act9010009

**AMA Style**

Dunst P, Hemsel T, Bornmann P, Littmann W, Sextro W. Optimization of Ultrasonic Acoustic Standing Wave Systems. *Actuators*. 2020; 9(1):9.
https://doi.org/10.3390/act9010009

**Chicago/Turabian Style**

Dunst, Paul, Tobias Hemsel, Peter Bornmann, Walter Littmann, and Walter Sextro. 2020. "Optimization of Ultrasonic Acoustic Standing Wave Systems" *Actuators* 9, no. 1: 9.
https://doi.org/10.3390/act9010009