# Experimental Study of Vibration Isolation Characteristics of a Geometric Anti-Spring Isolator
## 4 Experimental Study
### Linear Frequency Sweep Excitation Experiment  
Secondly, linear frequency sweep excitation signals are used to explore the nonlinearity of the designed geometric anti-spring isolator. Here, the low-frequency performance of the geometric anti-spring isolator is our subject. Thus the excitation frequency ranges from 1.5 Hz to 6 Hz and each sweep excitation experiment lasts 60 s once. Both upward and downward frequency sweep excitation experiments are carried out. Time history signals of both excitation acceleration and response acceleration under different excitation amplitudes are shown in Figure 10.  
Figure 9: The results of discrete sinusoidal excitation experiment. **(a)** The time domain signal at 5 Hz with excitation displacement of 0.6 mm. **(b)** The frequency domain signal at 5 Hz with excitation displacement of 0.6 mm. **(c)** Acceleration transmissibility for different excitation amplitudes: m = 21 kg. **(d)** Acceleration transmissibility for different mass loads with excitation amplitude of 0.6 mm. **(e)** The initial isolation frequency of the isolator. Figure 10: _Cont._  
With the growth of excitation amplitude, the acceleration response peak increases. Nonlinear jump phenomena are observed and vary with the increment of the excitation displacement amplitude. In Figure 10a, under the displacement excitation of 0.5 mm, both upward jumping and downward jumping phenomena of the response amplitude of load mass occurs in the neighbor of the resonance area under the upward frequency sweep excitation. For the situation of the downward frequency sweep excitation, only a downward jumping phenomena of the response signal is observed, which demonstrates a softening-type stiffness characteristic. When the excitation amplitude is 1.0 mm (Figure 10b), both the upward jumping and downward jumping phenomena of the response signal of the load mass exists under the upward frequency sweep excitation, which shows both hardening-type and softening-type nonlinearity. However, only upward jumping phenomenon of the response signal is found under the downward frequency sweep excitation. When the excitation amplitude is 1.5 mm, both the upward jumping and downward jumping phenomena are observed under upward and downward frequency sweep excitation. When the excitation amplitude increases to 2 mm, the nonlinearity is weak. There exists an upward jumping phenomenon under the upward frequency sweep excitation and a downward jumping phenomenon under the downward frequency sweep excitation, which demonstrates that the designed isolator has a softening-type stiffness characteristic. When the excitation amplitude is 2.5 mm or 3 mm, the response signals under both upward and downward frequency sweep excitation show an obvious downward jumping phenomenon. It can be seen that the designed isolator shows a complex nonlinearity. When the excitation amplitude is changed, both the hardening-type and softening-type stiffness characteristic can be observed. According to the acceleration signals in time domain, the acceleration transmissibility curve (Figure 11) of the geometric anti-spring isolator under the frequency sweep excitation can be calculated using the FFT transform. From Figure 11, it can be seen that the transmissibility curves show much difference in the resonance area between upward and downward frequency sweep excitation. The peak of the transmissibility curve under upward frequency sweep excitation is larger than that under downward frequency sweep excitation for all the excitation levels, which demonstrates that the designed geometric anti-spring isolator possesses a global hardening-type stiffness characteristic on the whole. The resonance frequency increases with the increment of the excitation amplitude. However, for different excitation amplitude, the characteristic of transmissibility shows obvious differences. As the excitation amplitude increases, the difference of transmissibility curve between the upward and downward frequency sweep excitation reduces first.