# Design of Longitudinal-Bending Coupled Horn of a Giant Magnetostriction Transducer

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## Abstract

**:**

## 1. Introduction

## 2. Materials and Methods

#### 2.1. Design of Longitudinal Vibration Horn

#### 2.1.1. Design Theory Based on Equivalent Four-Terminal Network

_{3}, the small cylindrical end of the horn, as shown in Figure 1 and Figure 2.

^{0.5}is the propagation velocity of the sound wave in the horn; E represents the elastic modulus of the material; ρ is the density of the material; k = ω/c is the circular wave number; z = ρcs represents the acoustic impedance of the cross-section; s is the cross-sectional area. The horn was made from non-magnetic materials to prevent magnetic leakage from affecting performance. In this article, 316 stainless steel was selected as the material for the horn, with the related parameters shown in Table 1.

#### 2.1.2. Modal Analysis

#### 2.2. Design of Bending Vibration Disc

#### 2.2.1. Design Theory

^{2}/12, S = D/k

^{2}Gt, ${e}_{0}^{4}=\rho {\omega}^{2}t/D$; D = Eh

^{3}/12(1 − ε

^{2}) is the bending stiffness constant of the thick disk. R and S represent the effects of rotational inertia and transverse shear deformation in the thick disk, respectively. k

^{2}= π/12; ε is the Poisson ratio, E is the elastic modulus, G = E/[2(1 + ε)] is the shear modulus; r, t, ρ, ω represent, respectively, the radius, thickness, density, angular frequency of the disk.

#### 2.2.2. Analysis of Rotating Wheel Model

#### 2.3. Dynamic Simulation of the L-BCH

#### 2.3.1. The Influence of the Rotating Wheel’s Thickness on the Dynamic Characteristics

#### 2.3.2. The Influence of the Spinning Wheel’s Large Diameter on the Dynamic Characteristics

#### 2.3.3. Influence of the Spinning Wheel’s Small Diameter on Dynamic Characteristics

#### 2.3.4. Influence of the Spinning Wheel’s Fillet Radius on Dynamic Characteristics

#### 2.4. Determination of Structural Parameters of the L-BCH

## 3. Result and Discussion

## 4. Conclusions

## Author Contributions

## Funding

## Institutional Review Board Statement

## Informed Consent Statement

## Data Availability Statement

## Conflicts of Interest

## References

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Parameters | Value |
---|---|

Large cylindrical segment length l_{1} (mm) | 30 |

Large cylindrical segment diameter d_{1} (mm) | 46 |

Conical segment length l_{2} (mm) | 30 |

Small cylindrical segment diameter d_{2} (mm) | 20 |

Young’s modulus E (GPa) | 193 |

Density ρ (kg/m^{3}) | 8000 |

Poisson ratio ν | 0.28 |

Parameters | Value |
---|---|

Corner radius, r (mm) | 2 |

Small diameter, d (mm) | 40 |

Large diameter, D (mm) | 80 |

Thickness, t (mm) | 16 |

Parameters | Value |
---|---|

Large cylindrical segment length l_{1} (mm) | 30 |

Large cylindrical segment diameter d_{1} (mm) | 46 |

Conical segment length l_{2} (mm) | 30 |

Small cylindrical segment length l_{3} (mm) | 51 |

Small cylindrical segment diameter d_{2} (mm) | 20 |

Young’s modulus E (GPa) | 193 |

Density ρ (kg/m^{3}) | 8000 |

Poisson ratio ν | 0.28 |

Small diameter d (mm) | 40 |

Large diameter D (mm) | 80 |

Thickness t (mm) | 14 |

corner radius r (mm) | 1 |

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**MDPI and ACS Style**

Li, P.; Chen, Y.; Li, W.; Sun, J.; Li, J.; Wang, K.
Design of Longitudinal-Bending Coupled Horn of a Giant Magnetostriction Transducer. *Actuators* **2022**, *11*, 110.
https://doi.org/10.3390/act11040110

**AMA Style**

Li P, Chen Y, Li W, Sun J, Li J, Wang K.
Design of Longitudinal-Bending Coupled Horn of a Giant Magnetostriction Transducer. *Actuators*. 2022; 11(4):110.
https://doi.org/10.3390/act11040110

**Chicago/Turabian Style**

Li, Pengyang, Yunshuai Chen, Wei Li, Jian Sun, Jian Li, and Kai Wang.
2022. "Design of Longitudinal-Bending Coupled Horn of a Giant Magnetostriction Transducer" *Actuators* 11, no. 4: 110.
https://doi.org/10.3390/act11040110