## 4 Penetration Test  
To further verify the validity and reliability of the TLE method proposed in this study, a test of projectile penetration into a semi-infinite concrete target was performed using a 152 mm caliber one-stage light-gas gun. The projectile was machined from 30 CrMnSiNi2A high-strength steel, and the necessary heat treatment was performed. Figure 8 shows the projectile geometry. The projectile had an ogive nose with caliber-radius-head (CRH) 3 and a nominal mass of 4.2 kg. A deceleration measurement device was attached to the projectile tail using a threaded connection for acquisition of the deceleration. An accelerometer and electronic components were sealed inside the test device. The structural material of the device housing should be the same as that of the projectile to avoid the influence of different contact surface stiffnesses on the deceleration signal. The specification of the thread body connecting the projectile and measuring device was M42 \(\times\) 2-6H/6g-33. The thread pitch and length were 2 and 33 mm, respectively. The sampling rate and trigger threshold of the accelerometer were set at 120 kHz and 8000 g, respectively, and a sleep time of 50 min was set to prevent false triggering of the measurement device. A C40 concrete target plate with a diameter of 120 cm and a thickness of 60 cm was used in the experiment. The measured unconfined compressive strength was 50 MPa. \begin{table}
\begin{tabular}{c c c c} \hline \hline
**Material** & \(E\) **(GPa)** & \(\
u\) & \(\rho\) (\(\mathbf{kg\cdot m^{-3}}\))** \\ \hline
45 steel & 211 & 0.269 & 7890 \\ \hline \hline \end{tabular}
\end{table} 
Table 6: Material parameters of the threaded tubes [24]. Figure 8: Projectile and target (units: mm) (source elaborated by authors). The projectile was accelerated along the gun barrel by the instant emission of high-pressure gas. After being separated from the sabots, the projectile impacted the concrete target plate vertically at a high speed of 320 m/s. The projectile target encounter conditions, including the striking velocity and incident attitude angle, were measured using a high-speed camera (Photron/SA5). The deceleration signal was acquired by a deceleration measurement device. The air pressure of the light-gas gun was adjusted to 4.4 MPa according to the projectile mass and striking velocity. After the experiment, the deceleration data in the acceleration data recorder were extracted. Figure 9 presents the deceleration-time curve in the experiment. In Figure 9, the raw experimental signal was low-pass filtered using cut-off frequencies of 40, 20, and 10 kHz. The results indicate that the signal frequency was concentrated within 40 kHz. Therefore, we selected the measured signal spectrum within 40 kHz for further research. Figure 10 shows the fast Fourier-transform (FFT) spectrum of the experimental deceleration signal. The first peak of the curve corresponds to the rigid body deceleration with a frequency of 354 Hz, indicating the response frequency of the projectile-fuse system to the penetration loading source. According to the classic theory of vibration, the dominant frequency of the penetration excitation signal is approximately 354 Hz. The rigid body deceleration was obtained by low-pass filtering of the experimental deceleration with a cut-off frequency of 1500 Hz (Figure 9). The rigid body deceleration represents the real-time resistance signal of the projectile nose. Figure 10 presents the FFT spectrum of rigid body deceleration (red solid line). It can be seen that only one peak exists in the FFT spectrum, with a peak frequency of 354 Hz. This confirms the hypothesis that the frequency of 354 Hz is the dominant frequency of the penetration excitation signal. Moreover, the frequencies at other peaks are roughly integer multiples of the base frequency (7919 Hz), indicating the existence of free vibration with a base frequency of 7919 Hz in the deceleration signal. Figure 10: FFT spectrum of the experimental curve (source elaborated by authors).