# Research on Semi-Active Vibration Control of Pipeline Based on Magneto-Rheological Damper
## 4 Experimental Study on Semi-Active Vibration Control  
### Pipeline Vibration Experiment Scheme  
The experimental system is mainly composed of pipeline, MR damper and its embedded drive control system, vibration signal detection system, vibration excitation device, power system and computer. The schematic diagram of the fluid dynamic pipeline vibration measurement and control system based on MR damper is shown in Figure 10.  
Here the servo electric cylinder is used to apply the excitation of different frequencies and amplitudes to the tested pipeline. The embedded vibration control system based on Digital Signal Processor (DSP) collects pipeline displacement signals and damper force signals from sensors. Then the optimal control force of pipeline vibration control is calculated according to the pipeline vibration control algorithm. Finally, the damping force of MR damper is controlled to reduce the vibration of pipeline. The pipeline vibration test system includes the acceleration sensor, INV3018A data acquisition instrument, vibration data acquisition and analysis software DASP to collect and analyze the pipeline vibration acceleration information. The laser displacement sensor, the tension pressure sensor, the NI6210 data collector and the Labview-based data acquisition software are selected to collect and  
Figure 9: Simulation of sliding-mode-variable-structure (SMVS) pipeline vibration control system: (a) Sliding-mode-variable-structure (SMVS) simulation model; (b) Vibration displacement response; (c) Control force and disturbance dynamics curve.  
record the pipeline vibration displacement and the MR damper control force. The pipeline vibration test platform is shown in Figure 11.  
The vibration level difference or the vibration attenuation rate is usually used as an indicator for evaluating the vibration control effect [20]. The vibration level difference of pipeline is 10 times of the logarithm of the square of the effective value of vibration response when the pipeline is uncontrolled and the square of the effective value of vibration response when the pipeline is controlled. Vibration response may be displacement, velocity or acceleration. Since the vibration speed of the pipeline cannot be directly measured, the displacement level difference and the acceleration level difference of the pipeline vibration can be expressed as:  
\[L_{x}=20\lg\frac{x_{u}^{rms}}{x_{c}^{rms}} \tag{32}\]  
\[L_{a}=20\lg\frac{a_{u}^{rms}}{a_{c}^{rms}} \tag{33}\]  
where \(x_{u}^{rms}\) and \(x_{c}^{rms}\) are the effective values of the vibration displacement when the pipeline is uncontrolled and controlled, respectively. Following this, \(a_{u}^{rms}\) and \(a_{c}^{rms}\) are the effective values of the vibration acceleration when the pipeline is uncontrolled and controlled, respectively.  
The vibration attenuation rate is the ratio of the difference between the effective values of the vibration response before and after the pipeline is controlled and the effective value of the vibration response when the pipeline is not controlled. The displacement attenuation rate and the acceleration attenuation rate can be expressed as:  
\[J_{x}=\frac{x_{u}^{rms}-x_{c}^{rms}}{x_{u}^{rms}}\times 100\% \tag{34}\]  
Figure 11: Pipeline vibration measurement and control system.  
Figure 10: Pipeline vibration measurement and control system based on MR damper.  
\[J_{a}=\frac{a_{u}^{rms}-a_{c}^{rms}}{a_{u}^{rms}}\times 100\% \tag{35}\]  
The vibration energy dissipation rate of the pipeline vibration control system can be expressed as:  
\[J_{e}=\frac{a_{u}^{rms}x_{u}^{rms}-a_{c}^{rms}x_{c}^{rms}}{a_{u}^{rms}x_{u}^{rms}} \times 100\% \tag{36}\]