*4.7. Sensitivity Analysis of the Natural Frequency of the Jet System to the Sti*ff*ness of the Spring in the Gun Head*

Let the initial gas content of the fluid be 0.02 and the fluid pressure be 0.6 MPa. When the stiffness of the spring in the gun head is in the range of 10–30 kN/m, the variation law of the first three natural frequencies and their sensitivities of the jet system with *k*<sup>5</sup> is shown in Figure 15.

**Figure 15.** The variation law of the first three natural frequencies and their sensitivities of the jet system with the stiffness of the spring in the gun head. (**a**) Variation law of natural frequency sensitivity. (**b**) Variation law of natural frequency.

It can be seen from Figure 15 that as the stiffness of the spring in the adaptive gun head increases, the first-order and second-order natural frequency sensitivities of the jet system monotonically decrease, the third-order natural frequency sensitivity monotonically increases, and their values are all positive. Corresponding to the change of natural frequency sensitivity of each order, the first three natural frequencies of the jet system gradually increase with the increase in spring stiffness, and the growth rate is small, which indicates that the spring stiffness of the gun head has little effect on the first three natural frequencies of the jet system and their sensitivities.

#### **5. Experimental Verification**

In order to verify the accuracy of the modal analysis of the jet system, a platform for the dynamic experiment of the fire-fighting jet system with adaptive gun head was built. The modal test of the working jet system was carried out by the hammering method. The experiment platform is shown in Figure 16. The experimental parameters are consistent with the parameters shown in Table 1.

**Figure 16.** Platform for dynamic experiment of the fire-fighting jet system with the adaptive gun head. (**a**) Prototype of gun head. (**b**) Experimental equipment.

The fast Fourier transform was used to analyze the acceleration signal output from the jet system in the frequency domain. The amplitude-frequency characteristics of the acceleration signal of the jet system under the action of the fluid self-pulsation excitation and the hammer step excitation are shown in Figure 17. The coordinate of point A in the Figure 17 is (19.5, 0.1438) and the coordinate of point B is (46.8, 0.1588).

**Figure 17.** Amplitude-frequency characteristic curve of the fire-fighting jet system with the adaptive gun head.

It can be seen from Figure 17 that the jet system has relatively obvious peaks at the frequencies of 19.5 Hz and 46.8 Hz, of which 46.8 Hz is the axial frequency of the centrifugal pump for the experimental system (2800 RPM) and 19.5 Hz is the first-order natural frequency of the jet system in the experiment. At the same time, due to the influence of fluid turbulence in the fire-fighting monitor, the amplitude-frequency curve superimposes the amplitude-frequency characteristics of white noise, which increases the difficulty of frequency spectrum recognition. Therefore, other order natural frequencies of the jet system cannot be determined experimentally. The experimental data and theoretical value of the first-order natural frequency of the jet system are shown in Table 4.

**Table 4.** Comparison between experimental data and theoretical value.


It can be seen from Table 4 that the theoretical first-order natural frequency is very close to the experimental data, and the error is only 0.51%, which verifies the accuracy of the proposed dynamic model of the fire-fighting jet system with the adaptive gun head.
