# The Influence of Sensor Size on Acoustic Emission Waveforms--A Numerical Study
## 3 Results  
### Surface Excitation  
Results analysis begins with the waveforms received due to surface excitation since it exhibits the highest interest in the sense that the response of the different sensors exhibits strong variations. Figure 2 shows the excited signal (two cycles sinusoid in yellow color at the start of the time axis) and the respective waveforms received by each sensor in the case of 1 MHz excitation frequency. The units of amplitude are arbitrary as they concern the linear regime. If the displacement source waveform peaks at 1, it can be considered that the maximum source displacement is 1 \(\upmu\)m. After the initial longitudinal wave arrivals noticed just after 15 \(\upmu\)s, the considerably stronger Rayleigh wave arrives. The higher Rayleigh amplitude is expected as this wave mode occupies the highest amount of energy after a surface excitation (approximately 67%, while only around 7% forms the longitudinal) [21]. Figure 1: Simulation model geometry. The \"point\" sensor (1 mm) registers quite clearly two strong cycles similar to the excited signal. However, the long sensor (20 mm) records a significantly distorted waveform: it consists of four small cycles interrupted by a plateau of nearly zero displacement. Looking at the displacement field of Figure 3a, corresponding to 22 \(\upmu\)s after excitation, the Rayleigh wave packet is entirely on the sensor line, creating a cancellation effect due to positive and negative peaks acting simultaneously. The Rayleigh wavelength of 1 MHz is 2.35 mm, while the length of two cycles is 4.70 mm, which is much smaller than the sensor size (20 mm). It is seen that if the entire wave packet is within the physical limits of the sensor, cancellation effect of the total output occurs. In contrast, this is not the case for the point sensor (1 mm) as a single wavelength cannot fit into the sensor size. The received waveform shape follows the peaks and valleys of the excited wave packet reaching higher amplitudes than the long sensor case. The waveform received by the medium sensor (5 mm) has mixed characteristics consisting of approximately 5 cycles of amplitude in between the other two cases. From a general assessment, it is obvious that the smaller the physical dimension of the sensor (respectively the line along which averaging is conducted), the higher the similarity between the excited and received waveform. Figure 3: (**a**) Snapshot of displacement field corresponding to 22 \(\upmu\)s 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 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). Differences are strong in the frequency domain as well, as seen in Figure 3b where the Fast Fourier Transforms (FFT) of the waveforms of Figure 2 are shown. Only the response of point sensor (1 mm) exhibits similarities to the actual FFT of the excited signal, with a clear higher peak at around 1 MHz. The responses of medium (5 mm) and long (20 mm) sensors neither have resemblance to the excited signal nor show strong content around 1 MHz. It is characteristic that the initial excited content centered around 1 MHz is distributed approximately evenly to the whole range of the first MHz for the long sensor. For AE damage characterization purposes, the latter observations are of utmost importance since the source excitation may be sensed by a severely distorted waveform on the receiver. The effect of sensor size modifies the output and influences the accuracy of the AE signal features and waveform shape in general. For lower frequencies, the differences in all aspects (waveform shape, FFTs) on sensors' response to horizontal surface source diminish and are minimized for the excitation frequency of 50 kHz (respective wavelength equal to 48 mm).