# Numerical and Experimental Validation of Active Vibration Control Logic Performance of a Hybrid Noise Control-Based Brick

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## Abstract

**:**

## 1. Introduction

## 2. Materials and Methods

## 3. Control Law Formulation

_{0}) is imposed at boundary x = 0 (Figure 3). The control law in terms of vibration velocity is imposed on the other boundary x = L. In order to maximise the absorption coefficient of the totally reflective right boundary, a displacement is generated at the controlled boundary:

_{0}the velocity imposed on the other boundary and j the imaginary part.

- The first one considers only a 2D tube and validates the MATLAB model.
- The second one considers a 2D simulation including a generic room in which the prototype could be placed instead of the loudspeaker in x = 0.
- The third one considers a 3D tube.

## 4. Experimental Validation

_{s}= 20,000 Hz and 20 tests are performed, lasting 2 s each. Then, the signals are processed in MATLAB, and the transfer function method is applied to obtain the total, incident and reflected pressure waves in the function of the position inside the tube.

_{s,acq}= 9 kHz, in order to comply with the performance of the dSpace. Figure 10 plots the schematic setup for the experiment in the active case.

_{m3}the position of the third microphone. The amplitude of this pressure, $\left|A\right|,$ is used to obtain the incident pressure in x = 0, which is given by:

_{0}and u

_{L}are obtained as:

## 5. Results and Discussion

## 6. Conclusions

## Author Contributions

## Funding

## Institutional Review Board Statement

## Informed Consent Statement

## Data Availability Statement

## Conflicts of Interest

## References

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**Figure 1.**Conceptual scheme of the 4-blocks component (with PDI behaviour) that creates the place where to insert the plate (in blue).

**Figure 4.**Closed–closed duct with control law maximising the absorption coefficient as boundary condition in the 2D MATLAB model: (

**a**) real part of the pressure field in Pascal and (

**b**) real part of the particle velocity field at f = 1000 Hz in m/s.

**Figure 5.**Simulation results of the 3D duct model in COMSOL: (

**a**) real part of the pressure field in Pascal and (

**b**) amplitude of the pressure field at f = 1000 Hz in Pascal.

**Figure 6.**Plate-patch system: (

**a**) transducer mounted directly to the plate surface. Such a configuration is referred to as a bonded configuration. The bonded configuration is an excellent choice for sensing or creating vibrations in a relatively stiff structure. Transducers in this configuration can be used to monitor vibrations caused by an outside source, section of the plate and (

**b**) axonometry of the tube with the applied piezoelectric patch represented by the radius where the moment is applied in the negative z-direction.

**Figure 7.**Updated model dimension: (

**a**) real part of the pressure field in Pascal and (

**b**) amplitude of the pressure field at f = 1000 Hz in Pascal.

**Figure 9.**Sound pressure reconstructed inside the impedance tube for the passive case at f = 1000 Hz: real part, with acoustic pressure in Pascal in Y axis and tube length in meters in X axis.

**Figure 13.**Simulation results of the 3D duct model in COMSOL: (

**a**) real part of the pressure field in the passive case in Pascal and (

**b**) real part of the pressure field in the active case in Pascal, (

**c**) particle velocity of the pressure field at f = 860 Hz in the passive case in m/s and (

**d**) particle velocity of the pressure field at f = 860 Hz in the active case in m/s. These results validate the control logic that maximises the absorption coefficients in the low-mid frequencies where the passive solutions are less effective.

Frequency [Hz] | Reflection Coefficient |
---|---|

100 | 1 |

125 | 1 |

160 | 0.85 |

200 | 0.94 |

250 | 0.95 |

315 | 0.97 |

400 | 0.87 |

500 | 0.91 |

630 | 0.91 |

800 | 0.93 |

1000 | 0.93 |

1250 | 0.93 |

1600 | 0.95 |

2000 | 0.94 |

Frequency [Hz] | Reflection Coefficient | Reduction |
---|---|---|

144 | 0.15 | 85.70% |

288 | 0.20 | 79.38% |

431 | 0.20 | 79.16% |

575 | 0.10 | 89.58% |

719 | 0.30 | 73.21% |

863 | 0.07 | 92.55% |

1007 | 0.15 | 83.51% |

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**MDPI and ACS Style**

Ronconi, I.; Salierno, R.; Liu, L.; Giglio, A.; Ripamonti, F.; Paoletti, I.
Numerical and Experimental Validation of Active Vibration Control Logic Performance of a Hybrid Noise Control-Based Brick. *Acoustics* **2022**, *4*, 720-732.
https://doi.org/10.3390/acoustics4030043

**AMA Style**

Ronconi I, Salierno R, Liu L, Giglio A, Ripamonti F, Paoletti I.
Numerical and Experimental Validation of Active Vibration Control Logic Performance of a Hybrid Noise Control-Based Brick. *Acoustics*. 2022; 4(3):720-732.
https://doi.org/10.3390/acoustics4030043

**Chicago/Turabian Style**

Ronconi, Ilaria, Roberta Salierno, Ling Liu, Andrea Giglio, Francesco Ripamonti, and Ingrid Paoletti.
2022. "Numerical and Experimental Validation of Active Vibration Control Logic Performance of a Hybrid Noise Control-Based Brick" *Acoustics* 4, no. 3: 720-732.
https://doi.org/10.3390/acoustics4030043