## 5 Experimental Investigations on the Ultra-Low-Frequency Broadband Characteristics  
To corroborate the theoretical results, this section is based on a five-period I-shaped radial metamaterial whose geometric parameters are as follows: the lattice constant \(a=20\) mm, the waist height \(h=20\) mm, the waist thickness \(d=12\) mm, and the average leg thickness \(e=4\) mm. Figure 17 shows the processing of the experimental sample. It is worth mentioning that the size parameters of the experimental sample are consistent with those in Figure 1c, to minimize the influence of the model on the experiment.  
In this paper, the radial metamaterial sample is adhered to the experimental bench to establish the surface constraint boundary conditions [36]. Subsequently, a quasi-static metamaterial is formed, as shown in Figure 18. Using the M + P dynamic analysis system, the vibration energy decay curve of the quasi-static experimental sample is collected, and the existence of the ultra-low-frequency broadband is verified. A pulsing hammer to make the sample vibrate is used. Subsequently, the vibration sensor installed in a specific position transmits the vibration displacement of the pulse hammer and the sample to the vibration analyzer. After the analysis and the calculation, the vibration energy attenuation curve of the tested sample is obtained.  
Figure 16: Von Mises stress distribution (**a**) without the metamaterial and (**b**) with the metamaterial.  
Figure 17: Experimental specimen of the I-shaped metamaterial plate: (**a**) side view and (**b**) front view.  
In this experiment, the transient excitation method of the hammer is adopted by using the vibration sensor to pick up multiple sets of data independently. To ensure the validity of the experimental data, the data are averaged. The experimental results are shown in Figure 19.  
Figure 19 shows the experimental and simulated frequency response curves of the specimen. The results show that a large attenuation region appears at 0.1-1012 Hz. The initial frequency of the band gap is in good agreement with the experimental results, but there is a discrepancy between the cut-off frequencies of the simulation results and experimental results. The main reason for the discrepancy is that the fixed boundary conditions, as specified in the theoretical method, cannot be fully guaranteed on the installation method of the specimen in the vibration experiment. In the finite element model, the base surface is a fixed constraint boundary condition, but the installation method of the specimen in the experiments cannot completely guarantee the realization of the constraint boundary conditions of the base surface. In the experimental structure, the cut-off frequency is shifted to the low frequency because the existence of damping at the sensor connection dissipates the natural vibration energy of the system. Therefore, the cut-off frequency exhibits a certain error. Furthermore, the materials (epoxy) in the simulation  
Figure 19: Specimen frequency response curve.  
Figure 18: Experimental test system.  
are all linear elastic, homogeneous, and isotropic. However, they are not perfect ideal models for the experiments. Although there are some differences between the experimental results and the simulation results, they both indicate the existence of ultra-low-frequency broadband. The simulation results are, therefore, consistent with the experimental results.