# Aeroelastic Stability Analysis of Electric Aircraft Wings with Distributed Electric Propulsors

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## Abstract

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## 1. Introduction

## 2. Problem Statement

## 3. The Mathematical Model

## 4. Verification and Results

## 5. Conclusions

## Author Contributions

## Funding

## Institutional Review Board Statement

## Informed Consent Statement

## Data Availability Statement

## Conflicts of Interest

## References

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**Figure 1.**NASA’s X-57 Maxwell aircraft [8].

**Figure 3.**Comparison of the flutter speed of the wing with one engine for $\lambda =1$. $\nu $ is the nondimensional flutter speed, and p is the nondimensional engine thrust.

**Figure 4.**The effect of the tip propulsor thrust and angular momentum on the flutter speed of the wing (case 1).

**Figure 5.**The effect of tip propulsor thrust and angular momentum on the flutter frequency of the wing (case 1).

**Figure 6.**The effect of the tip propulsor thrust and angular momentum on the flutter speed of the wing (case 2).

**Figure 7.**The effect of the tip propulsor thrust and the angular momentum on the flutter frequency of the wing (case 2).

**Figure 8.**The effect of the tip propulsor thrust, angular momentum, and mass on the flutter speed of the wing (case 2).

**Figure 9.**The effect of the tip propulsor thrust, angular momentum, and mass on the flutter frequency of the wing (case 2).

Parameter | Value |
---|---|

Wing length | 6.1 m |

Semi-chord | 1.83 m |

Bending rigidity | 9.77 $\times {10}^{6}$ N.m${}^{2}$ |

Torsional rigidity | 0.99 $\times {10}^{6}$ N.m${}^{2}$ |

Mass per unit length | 35.7 kg/m |

Wing moment of inertia per unit length | 8.64 kg.m |

Elastic axis offset from L.E | 33% chord |

Centre of gravity offset from L.E. | 43% chord |

Aerodynamic centre offset from L.E. | 25% chord |

$d{x}_{1},d{x}_{2},\dots ,d{x}_{6}$ | 0.76 m |

$d{x}_{t}$ | 1.52 m |

Mass of high-lift motors | 10 kg |

Mass of tip propulsor | 26 kg |

${C}_{{l}_{\alpha}}$ | 2$\pi $ |

Nominal thrust of high-lift motors | 400 N |

Nominal angular momentum of high-lift motors | 156 kg.m${}^{2}$.rad/s |

Nominal thrust of tip propulsor | 2507 N |

Nominal angular momentum of tip propulsor | 5000 kg.m${}^{2}$.rad/s |

Predicted Quantity | Equipped Wing | Clean Wing |
---|---|---|

Flutter speed (m/s) | 155 | 136 |

Flutter frequency (rad/s) | 71 | 70 |

Predicted Quantity | Case 1 | Case 2 | All Motors Off |
---|---|---|---|

Flutter speed (m/s) | 155 | 152 | 154 |

Flutter frequency (rad/s) | 71 | 71 | 71 |

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**MDPI and ACS Style**

Amoozgar, M.; Friswell, M.I.; Fazelzadeh, S.A.; Haddad Khodaparast, H.; Mazidi, A.; Cooper, J.E.
Aeroelastic Stability Analysis of Electric Aircraft Wings with Distributed Electric Propulsors. *Aerospace* **2021**, *8*, 100.
https://doi.org/10.3390/aerospace8040100

**AMA Style**

Amoozgar M, Friswell MI, Fazelzadeh SA, Haddad Khodaparast H, Mazidi A, Cooper JE.
Aeroelastic Stability Analysis of Electric Aircraft Wings with Distributed Electric Propulsors. *Aerospace*. 2021; 8(4):100.
https://doi.org/10.3390/aerospace8040100

**Chicago/Turabian Style**

Amoozgar, Mohammadreza, Michael I. Friswell, Seyed Ahmad Fazelzadeh, Hamed Haddad Khodaparast, Abbas Mazidi, and Jonathan E. Cooper.
2021. "Aeroelastic Stability Analysis of Electric Aircraft Wings with Distributed Electric Propulsors" *Aerospace* 8, no. 4: 100.
https://doi.org/10.3390/aerospace8040100