# Experimental Study of Vibration Isolation Characteristics of a Geometric Anti-Spring Isolator
## 4 Experimental Study
### Discrete Sine Excitation Experiment  
First, the discrete sine excitation signal is used to investigate the vibration isolation performance of the designed geometric anti-spring isolator. The excitation frequency ranges from 1.8 Hz to 10 Hz and increases step by step with a frequency interval of 0.1 Hz. The acceleration signals are acquired by accelerometers after the response signals of the load mass are steady at each discrete excitation frequency. The spectrum of response acceleration is calculated using FFT (Fast Fourier Transform). The acceleration signal at 5 Hz under an excitation displacement amplitude of 0.6 mm is given in Figure 9. Both time history (Figure 9a) and spectrum results (Figure 9b) are presented. It can be seen that the responsive frequency domain signal includes the components of harmonic frequencies. Except for the excitation frequency component of 5 Hz, there exist the frequency components of 10 Hz and 15 Hz, which demonstrates that the nonlinearity exists in the geometric anti-spring isolator.  
The acceleration transmissibility curves under different excitation amplitude and different mass load were shown in Figure 9c-d. From the Figure 9c, it is obvious that the transmissibility of the geometric anti-spring isolator under the load mass of 21 kg in resonance area increases with the increment of excitation amplitude. Resonance frequencies under different excitation amplitude are approximate to be 2.4 Hz. When the excitation frequency is larger than 3.6 Hz, transmissibility values of the geometric anti-spring isolator are smaller than 1 and the vibration of load mass is attenuated. When excitation amplitude is 0.8 mm, the acceleration transmissibility is 0.59 (4.5 dB) at the excitation frequency of 4 Hz and 0.11 (19 dB) at the excitation frequency of 8 Hz.  
From Figure 9d, it can be seen that an apparent shift of resonance frequency of the geometric anti-spring isolator is observed for different load masses, of which the excitation amplitude is 0.6 mm. The load mass ranges from 16 kg to 26 kg with a mass interval of 2.5 kg. As the mass load increases, the resonance frequency first decreases and then increases. The minimum resonance frequency is 2.4 Hz under the load mass of 21 kg. When the load mass is 21 kg, the vibration isolation performance is better than that of other load masses. However, it can be seen that the attenuation rate of transmissibility slightly grow as load mass goes away from 21 kg. When the excitation frequency is 8 Hz, the transmissibility of the geometric anti-spring isolator for different load masses (16 kg, 18.5 kg, 21 kg, 23.5 kg and 26 kg) is 0.21 (13.6 dB), 0.15 (16.5 dB), 0.12 (18.4 dB), 0.15 (16.5 dB) and 0.18 (14.9 dB), respectively. These results match well with the change of the resonance frequency of the geometric anti-spring isolator for different load masses.  
Figure 9e shows the initial isolation frequency of the geometric anti-spring isolator for different excitation amplitudes and load masses. With the increment of the excitation displacement amplitude, the initial isolation frequency approximately linearly decreases. When the excitation displacement amplitude is 2 mm, the initial isolation frequency reaches to 3.18 Hz. For the situation of different load mass, the initial isolation frequency decreases first and then increases as the load mass increases. The minimum initial isolation frequency under excitation displacement amplitude of 0.6 mm is 3.5 Hz with the load mass of 21 kg.