# Multiharmonic Resonance Control Testing of an Internally Resonant Structure

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## Abstract

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## 1. Introduction

- Detect the presence of nonlinearity, and establish the need for a nonlinear approach.
- Identify the coefficients that parametrise nonlinearity to give an optimal fit to experimental data.
- Evaluate the quality of the fitted model and make predictions with it.

## 2. Generalising Phase for Multiharmonic Excitation

## 3. Feedforward Control of Resonance

## 4. Programming the Test Sweep

#### 4.1. Hybrid Voltage/Resonant Control Strategy

#### 4.2. Isolas

## 5. Experimental Test Rig

#### 5.1. System under Test

#### 5.2. Data Acquisition and Control

#### 5.3. Settling Algorithm

## 6. Results

#### 6.1. Typical Resonance Seen in a Force Control Sweep

#### 6.2. Resonance Control Tests

#### 6.3. Effect of Target Resonance Level

#### 6.4. Effect of Different Levels of Harmonic Control

#### 6.5. Changes to the Structure under Test

## 7. Conclusions and Future Work

## Author Contributions

## Funding

## Conflicts of Interest

## References

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**Figure 4.**Results of a force control sweep, fundamental force amplitude 2.75 N, third harmonic force amplitude set to zero through feed forward control; other harmonics not controlled.

**Figure 5.**Resonance controlled frequency sweeps, with voltage excitation applied at the fundamental frequency and third harmonic (small markers indicate third harmonic values).

**Figure 6.**Resonance controlled frequency sweeps, with voltage excitation applied at the fundamental and third harmonic frequencies (small markers indicate third harmonic values).

**Figure 7.**Resonance controlled frequency sweeps with different levels of harmonic control, ${\Psi}_{0}=0.5$ (Small markers indicate third harmonic values).

**Figure 8.**Resonance controlled frequency sweeps, with different levels of harmonic control, ${\Psi}_{0}=0.75$ (Small markers indicate third harmonic values).

**Figure 9.**Effect of variation of the spring tension in the nonlinear mechanism on resonance control sweeps, ${\Psi}_{0}=0.75$.

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## Share and Cite

**MDPI and ACS Style**

Shaw, A.D.; Hill, T.L.; Neild, S.A.; Friswell, M.I.
Multiharmonic Resonance Control Testing of an Internally Resonant Structure. *Vibration* **2020**, *3*, 217-234.
https://doi.org/10.3390/vibration3030017

**AMA Style**

Shaw AD, Hill TL, Neild SA, Friswell MI.
Multiharmonic Resonance Control Testing of an Internally Resonant Structure. *Vibration*. 2020; 3(3):217-234.
https://doi.org/10.3390/vibration3030017

**Chicago/Turabian Style**

Shaw, Alexander D., Thomas L. Hill, Simon A. Neild, and Michael I. Friswell.
2020. "Multiharmonic Resonance Control Testing of an Internally Resonant Structure" *Vibration* 3, no. 3: 217-234.
https://doi.org/10.3390/vibration3030017