# Effect of Wind-Induced Vibration on Measurement Range of Microcantilever Anemometer

^{*}

^{†}

## Abstract

**:**

## 1. Introduction

## 2. Principle and Design

_{v}), the deflection w(x) of the flexible substrate can be expressed by [15]

_{D}, ρ

_{air}, W are the coefficient of drag force, the air density, and the cantilever width, respectively. Hence, the deflection w(x) of the flexible substrate can be given by

_{v}), the airflow-induced vibration will happen. As a result, the Bernoulli equation becomes useless to predict the motion of the cantilever. According to the theory of continuous system vibration, the motion equation for the transverse vibration of the cantilever can be given by [15]

_{can}, and A are the time-dependent transverse deflection, the cantilever density, and the cross-sectional area of the cantilever, respectively. For microcantilevers, it is vortex-induced vibration that causes the shake of the output [17]. When an airflow acts on the cantilever, periodic shedding of vortices will appear. The corresponding vortex shedding frequency f

_{v}is expressed by [17,18]

_{t}is the Strouhal number, which depends on the shape of the cantilever and is typically 0.15–0.25 for an arbitrary shape. D is the windward-side characteristic size of the cantilever. The shedding of vortices causes a fluid oscillation force with frequency f

_{v}, resulting in the cantilever vibration. When the trigger frequency f

_{v}is close to the natural frequency f

_{o}of the cantilever, the vortex-induced vibration will occur, which means

_{o}of the cantilever can be written as [15,19]

_{n}l is constant, which is expressed by

_{v}of the cantilever can be written as

_{v}is proportional to T and E

^{1/2}, and inverse proportional to L. Therefore, to improve the critical speed, one can then look into three directions: increasing cantilever thickness T, increasing elasticity modulus E, and reducing cantilever length L.

## 3. Experiment and Discussion

## 4. Conclusions

## Author Contributions

## Funding

## Acknowledgments

## Conflicts of Interest

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**Figure 1.**The microcantilever anemometer fabricated by our group, and the effect of wind-induced vibration on the output response of the anemometer under different wind speeds.

**Figure 2.**Schematic overview of the microcantilever anemometer under different wind speeds: (

**a**) no wind, (

**b**) lower than the critical speed, (

**c**) higher than the critical speed.

**Figure 3.**Schematic diagram of the measurement setup and the photograph of the fabricated microcantilever anemometer prototype.

**Figure 4.**Experimental output voltage versus wind speed characteristics for prototypes with different lengths.

**Figure 5.**Experimental output voltage versus wind speed characteristics for prototypes with different thicknesses.

**Figure 6.**Experimental output voltage versus wind speed characteristics for prototypes with different substrate Young’s modulus.

**Figure 7.**Experimental output voltage versus wind speed characteristics for the anemometers with or without vibration suppression capability.

No. | Length (L) (mm) | Width (W) (mm) | Thickness (T) (mm) | Young’s Modulus (GPa) |
---|---|---|---|---|

1 | 20 | 15 | 0.2 | 2.0 |

2 | 25 | 15 | 0.2 | 2.0 |

3 | 30 | 15 | 0.2 | 2.0 |

4 | 35 | 15 | 0.2 | 2.0 |

5 | 40 | 15 | 0.2 | 2.0 |

6 | 30 | 15 | 0.3 | 2.0 |

7 | 30 | 15 | 0.4 | 2.0 |

8 | 30 | 15 | 0.5 | 2.0 |

9 | 30 | 15 | 0.6 | 2.0 |

10 | 30 | 15 | 0.2 | 2.3 |

11 | 30 | 15 | 0.2 | 3.3 |

12 | 30 | 15 | 0.2 | 3.8 |

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**MDPI and ACS Style**

Ye, Y.; Wan, S.; He, X.
Effect of Wind-Induced Vibration on Measurement Range of Microcantilever Anemometer. *Micromachines* **2022**, *13*, 720.
https://doi.org/10.3390/mi13050720

**AMA Style**

Ye Y, Wan S, He X.
Effect of Wind-Induced Vibration on Measurement Range of Microcantilever Anemometer. *Micromachines*. 2022; 13(5):720.
https://doi.org/10.3390/mi13050720

**Chicago/Turabian Style**

Ye, Yizhou, Shu Wan, and Xuefeng He.
2022. "Effect of Wind-Induced Vibration on Measurement Range of Microcantilever Anemometer" *Micromachines* 13, no. 5: 720.
https://doi.org/10.3390/mi13050720