# The Influence of Sensor Size on Acoustic Emission Waveforms—A Numerical Study

^{*}

## Abstract

**:**

## 1. Introduction

## 2. Numerical Simulation

_{x}and u

_{y}components), ρ is the density (kg/m

^{3}), λ and μ are the first and second Lamè constants (Pa), h and $\phi $ are the “shear” and “bulk” viscosity (Pa·s) and t is time (s) [19].

^{3}. Concrete was chosen as the most representative example of widely applied structural material used in bulk geometries, as metals and composites are usually formed in plates and the propagation conditions differ.

## 3. Results

#### 3.1. Surface Excitation

#### 3.2. Vertical Excitation Beneath the Sensor

#### 3.3. Diagonal Excitation

## 4. Discussion

#### 4.1. Impact of Sensor Size on Signal Amplitude

#### 4.2. Effect of Wavelength over Sensor Size

#### 4.3. Impact of Sensors Size Effect on Frequency Content

_{xy}”. This function is given by:

#### 4.4. Experimental Evidence

## 5. Secondary Effects

## 6. Conclusions

## Acknowledgments

## Author Contributions

## Conflicts of Interest

## References

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**Figure 2.**Waveforms received by different size sensors for the case of surface source and excitation frequency of 1 MHz. The excitation wave (yellow starting at time 0) was reduced to the graph axes for clarity (nominal amplitude of 1).

**Figure 3.**(

**a**) Snapshot of displacement field corresponding to 22 μs after excitation (frequency at 1 MHz). The source is set on the surface; (

**b**) Fast Fourier Transforms (FFT) functions of the waveforms received by different size sensors.

**Figure 4.**(

**a**) Waveforms received by different size sensors for the case of surface source and excitation frequency of 50 kHz; (

**b**) FFT functions of waveforms received by different size sensors (exc. frequency at 50 kHz and surface source). The corresponding waveforms are depicted in Figure 4a.

**Figure 5.**(

**a**) Waveforms received by different size sensors for the case of vertical source and excitation frequency of 1 MHz; (

**b**) Waveforms received by different size sensors for the case of vertical source and excitation frequency of 50 kHz.

**Figure 6.**(

**a**) Waveforms received by different size sensors for the case of diagonal source and frequency excitation of 1 MHz; (

**b**) Snapshot of displacement field corresponding to 10 μs after excitation (exc. frequency at 1 MHz).

**Figure 7.**(

**a**) FFT functions of waveforms received by different size sensors (exc. frequency at 1 MHz and diagonal source); (

**b**) FFT functions of waveforms received by different size sensors (exc. frequency at 50 kHz and diagonal source).

**Figure 8.**Relative amplitude of the received signal for point (1 mm, in grey), medium (5 mm, in blue), long (20 mm, in red) along the frequency range, from 50 kHz to 1 MHz, and concerning the three source positions: (

**a**) surface; (

**b**) diagonal; (

**c**) vertical.

**Figure 10.**(

**a**) Waveforms received by the 5 mm size sensor emitted from source set on the surface (in black) and vertically beneath the sensor (in blue) with excitation frequency equal to 1 MHz. Original waveform is added in red color and in reduced scale to fit the graph; (

**b**) Respective coherence functions between received waves and original.

**Figure 11.**Average coherence up to 2 MHz for different sensor size and angles of propagation relatively to the sensor surface and excitation frequencies (

**a**) 1 MHz; (

**b**) 500 kHz.

**Figure 12.**Experimental setup showing the receiver at the top concrete surface and pencil lead breakage applied at the horizontal and vertical direction.

**Figure 13.**Individual waveforms received by Pico (5 mm) sensor in the case of (

**a**) horizontal excitation; (

**b**) vertical (

**c**) the average FFT curves of previous waveforms.

**Figure 14.**Waveforms received by long size (R15, 20 mm) sensor in the case of (

**a**) horizontal surface; (

**b**) vertical excitation; (

**c**) The average FFT curves of previous waveforms.

**Figure 15.**(

**a**) Simulated waveforms received by 20 mm size sensor after surface source excitation with frequency of 500 kHz and different number of cycles; (

**b**) Relative amplitude vs. waveform length over sensor size.

**Figure 16.**Simulated waveforms received by different size sensors from surface source with excitation frequency equal to 500 kHz (curves overlap).

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**MDPI and ACS Style**

Tsangouri, E.; Aggelis, D.G. The Influence of Sensor Size on Acoustic Emission Waveforms—A Numerical Study. *Appl. Sci.* **2018**, *8*, 168.
https://doi.org/10.3390/app8020168

**AMA Style**

Tsangouri E, Aggelis DG. The Influence of Sensor Size on Acoustic Emission Waveforms—A Numerical Study. *Applied Sciences*. 2018; 8(2):168.
https://doi.org/10.3390/app8020168

**Chicago/Turabian Style**

Tsangouri, Eleni, and Dimitrios G. Aggelis. 2018. "The Influence of Sensor Size on Acoustic Emission Waveforms—A Numerical Study" *Applied Sciences* 8, no. 2: 168.
https://doi.org/10.3390/app8020168