## 5 Experimental Validation and Further Optimization of Vibration Properties Method  
For the main structure of the proposed metamaterials, the bandgap properties can be adjusted by adopting different materials for the pins. However, the density of the metal pins is not continuous, which results in an altered discontinuity of the bandgap frequency. Furthermore, the vibration suppression in the low-frequency band has always been a concern in engineering applications; to be precise, scholars have been widely interested in the ability of metamaterials to suppress low-frequency vibrations, especially to below 2000 Hz. Unfortunately, the bandgap effect of the CDCHM is still not ideal at low frequencies after the introduction of chiral structures, and new optimization methods need to be explored in addition to adding metal pins. According to the modal theory and the above research on the vibration properties of the metamaterials, adding dense materials to the structure of the CDCHM can simultaneously improve the bearing capacity and vibration-suppression performance. Moreover, according to the modes of the metamaterial, it can be found that the vibration deformation of the chiral structure in the low-frequency region is mainly the local resonance based on the metal pins. Therefore, an optimization method of using particle damping to suppress the vibration of the metamaterial is proposed, and the metal tube with particle damping is introduced into the rings of the CDCHM. In order to further explore the vibration-suppression ability of the CDCHM and the optimization approach, and verifying the effectiveness and accuracy of the COMSOL and ABAQUS simulation methods, the vibration transmission loss of the proposed metamaterials was tested on the experimental system. Figure 11 shows the experimental system. The input and output signals of the two equipped acceleration sensors were collected at a frequency of 10 kHz, and the signals were converted and transmitted to the computer by the signal converter. The shaker realized the white noise excitation signal generated from the signal generator, and the sweep frequency range was from 2 Hz to 2500 Hz. To more clearly show the trend of the test results, a Kalman filter was designed to process the experimental data. Figure 10: The influence of materials of pins on bandgap: (**a**) structure diagram of the CDCHM; (**b**) aluminum; (**c**) copper; (**d**) tungsten; (**e**) vibration mode of the first gap. In this section, a metal tube with particle damping is introduced into the CDCHM to achieve better vibration suppression. Firstly, the vibration characteristics of the proposed metamaterials are tested to verify the simulations. Subsequently, the vibration characteristics of the CDCHM with particle damping are investigated by the experiments. Figure 12 represents the bandgaps (green color bars) from the simulation and the VTL based on the experiment. As indicated from Figure 12a, the first bandgap suppresses the increasing vibration. Due to the introduction of the chiral structure, the CDCHM has a narrow first bandgap at around 2700 Hz, which is similar to the effect of a dynamic vibration absorber, and the two bandgaps of the CDCHM within 5000 Hz are located near the trough of the VTL curve, as shown in Figure 12b. Figure 12c shows the experiment and simulation results of the CDCHM with the copper pins. It can be seen that the first bandgap is at the attenuation part of the VTL curve. Since the second and third bandgaps are narrow and there is a gap between them, the variation in the VTL curve is not large. Furthermore, the value of the VTL here is close to \(-20\) dB, so it can be considered that the test and simulation correspond to each other. The fourth bandgap in Figure 12c is in the second half of the VTL curve depression, which is caused by the characteristics of the structure itself.