# Influence of System and Actuator Nonlinearities on the Dynamics of Ring-Type MEMS Gyroscopes

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## Abstract

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## 1. Introduction

## 2. Governing Equations

## 3. Development of Nonlinear Electrostatic Force Model for MEMS Ring-Based Gyroscope

## 4. Results and Discussion

#### 4.1. Natural Frequency Variation

#### 4.2. Time Response

## 5. Conclusions

## Author Contributions

## Funding

## Data Availability Statement

## Acknowledgments

## Conflicts of Interest

## Appendix A

## References

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**Figure 6.**Radial displacement in driving direction for ${A}_{\mathrm{n}}$ for $\Omega =2\pi \mathrm{rad}/\mathrm{s}$ in presence of nonlinear parameter $\gamma $.

**Figure 7.**Radial displacement in the sensing direction ${B}_{\mathrm{n}}$ for $\Omega =2\pi \mathrm{rad}/\mathrm{s}$ in presence of nonlinear parameter $\gamma $.

**Figure 8.**Phase diagram in driving direction ${A}_{\mathrm{n}}$ for $\Omega =2\pi \mathrm{rad}/\mathrm{s}$ in presence of nonlinear parameter $\gamma $.

**Figure 9.**Phase diagram in sensing direction ${B}_{\mathrm{n}}$ for $\Omega =2\pi \mathrm{rad}/\mathrm{s}$ in presence of nonlinear parameter $\gamma $.

**Figure 10.**Poincare’ map in driving direction ${A}_{\mathrm{n}}$ for $\Omega =2\pi \mathrm{rad}/\mathrm{s}$ in presence of nonlinear parameter $\gamma $.

**Figure 11.**Poincare’ map in sensing direction ${B}_{\mathrm{n}}$ for $\Omega =2\pi \mathrm{rad}/\mathrm{s}$ in presence of nonlinear parameter $\gamma $.

**Figure 12.**Poincare’ map in driving direction ${A}_{\mathrm{n}}$ for $\Omega =2\pi \mathrm{rad}/\mathrm{s}$ in absence of nonlinear parameter $\gamma $.

**Figure 13.**Poincare’ map in sensing direction ${B}_{\mathrm{n}}$ for $\Omega =2\pi \mathrm{rad}/\mathrm{s}$ in absence of nonlinear parameter $\gamma $.

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**MDPI and ACS Style**

Gebrel, I.F.; Asokanthan, S.F.
Influence of System and Actuator Nonlinearities on the Dynamics of Ring-Type MEMS Gyroscopes. *Vibration* **2021**, *4*, 805-821.
https://doi.org/10.3390/vibration4040045

**AMA Style**

Gebrel IF, Asokanthan SF.
Influence of System and Actuator Nonlinearities on the Dynamics of Ring-Type MEMS Gyroscopes. *Vibration*. 2021; 4(4):805-821.
https://doi.org/10.3390/vibration4040045

**Chicago/Turabian Style**

Gebrel, Ibrahim F., and Samuel F. Asokanthan.
2021. "Influence of System and Actuator Nonlinearities on the Dynamics of Ring-Type MEMS Gyroscopes" *Vibration* 4, no. 4: 805-821.
https://doi.org/10.3390/vibration4040045