# Semi-Active Vibration Control Based on a Smart Exciter with an Optimized Electrical Shunt Circuit
## 3 Numerical Analysis of Vibration Reduction Potential
### Numerical Evaluation of Vibration Reduction Potential  
#### 3.2.1 Analysis of Wideband Effect by Simulation of Step Response Behavior  
After modeling the panel-SE-RL-shunt system successfully, the vibration reduction effect has been simulated numerically. It turned out that both the series connection and the parallel connection of the resistor and inductor have a similar effect on vibration reduction. For this reason, only the results for the SE with the RL-shunt in series connection will be discussed in detail. A SE coupled at position P2 is taken into account. First, the wideband effect has been investigated by using a step signal as input for the Simulink model. The results from the scope blocks are shown in Figure 6a,b. Figure 6a shows displacement vs.  
Figure 4: Block diagram representing the SE with the RL-shunt.  
Figure 5: Fully coupled time-domain model for the panel with the smart exciter including the RL-shunt.  
time for the panel without the SE, and Figure 6b represents the panel with the SE. The coordinates of the three positions used for evaluation are shown in Figure 3.  
In Figure 6, the blue curves represent the displacement of position P2, which is the position with the greatest amplitude of displacement. The black curves show displacement of position P1, which has the smallest amplitude. The red curves are for position P3. The displacement amplitude at this position is between the amplitude observed at the positions P2 and P1. After comparing Figure 6a,b, we find that the initial conditions at t = 1 s (time of step input) are identical for both systems. We also find that the SE with the RL-shunt can reduce the vibrations in a short period of time. Amplitude reduction seen in the curves in Figure 6b occurs in almost 0.1 s, whereas in Figure 6a, the same process takes almost 10 s. Comparing the results in the time intervals t = 1 s and t = 10 s, it is obvious that the amount of damping is significantly increased for the system with the SE.  
Additionally, the frequency response of the panel has been observed. The amplitude response is shown in Figure 7. According to the legend, the black curves are for position P1, and the blue and red curves are for positions P2 and P3. In Figure 7a, we can find that 142.2, 290.5, 419.6 and 567.3 Hz are the first four dominating natural frequencies of the panel. A resonance at 540 Hz is of lower magnitude. After comparing Figure 7a,b, we see that the vibration reduction effect is most significant at the first natural frequency,  
Figure 6: Displacement vs. time of the panel at positions P1, P2 and P3 (compare Figure 3): (**a**) without the SE and (**b**) with the SE.  
whilst at the other three natural frequencies, the amplitude remains nearly unchanged. This may be due to the coupling position of the SE at position P2 in the center of the panel. The displacement of the panel center point reaches a maximum in the dominant first eigenmode. Therefore, the maximum of vibration reduction (semi-active vibration damping) also occurs at this first natural frequency. In total, the magnitude is reduced from \(-101.6\) dB down to \(-134.3\) dB at position P2.  
Naturally, the dynamical behavior of the panel with the SE differs from the behavior of the panel without the SE. As a consequence, the first natural frequency is reduced from \(142.2\) Hz down to \(118.4\) Hz, as shown in Figure 7. Since the SE is attached at position P2, the mode shape associated with the first natural frequency is significantly suppressed.