# Revealing the Dynamic Characteristics of Composite Material-Based Miura-Origami Tube

^{*}

## Abstract

**:**

## 1. Introduction

## 2. Materials and Methods

#### 2.1. Geometric Design of the Miura Tube

#### 2.1.1. Miura Sheet

#### 2.1.2. Miura Tube

#### 2.2. Finite Element Modelling

## 3. Results and Discussion

#### 3.1. The Natural Frequency

#### 3.1.1. Effects of Structural Parameters on the Natural Frequency (NF)

#### 3.1.2. Effects of Material Parameters on the Natural Frequency

_{0}= 0.2 mm, i.e., the thickness of the material sheet was 0.6 mm, and the layers were bonded. The laying Angle of carbon fiber in each layer in each scheme is shown in Figure 4. The numerical simulation results are presented in Table 3.

#### 3.2. Study on Dynamic Displacement Response

#### 3.2.1. Effects of the Wall Thickness on the DDR

#### 3.2.2. Effects of the folding angle θ on the DDR

#### 3.2.3. Effects of the Parallelogram Side Length Ratio a/b on the DDR

^{−5}mm) when a/b = 1.8. Figure 7b shows that as a/b gradually increased, the displacement response gradually decreased. When a/b = 1, the displacement response reached a maximum value of 0.1708 mm. Figure 7c displays that as the a/b gradually increased, the displacement response gradually decreased. When a/b = 1, the displacement response reached a maximum value of 0.3763 mm. It was also found that the xOy out-of-plane stiffness was the smallest, compared with the other two, meaning that designers need to pay special attention to this stiffness when designing lightweight structures. Of course, this result also provides an effective method for designers to improve such stiffness.

#### 3.3. Effects of the Number of Arrangements of Miura Sheet Units

## 4. Conclusions

## Author Contributions

## Funding

## Institutional Review Board Statement

## Informed Consent Statement

## Data Availability Statement

## Acknowledgments

## Conflicts of Interest

## References

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**Figure 1.**Construction of a Miura tube model: (

**a**) geometric model of Miura sheet unit, (

**b**) geometric model of a Miura sheet (consisting of four Miura sheet units), and (

**c**) geometrical model of a Miura tube (consisting of two identical Miura sheets).

**Figure 2.**(

**a**–

**c**) illustrate the concentrated forces along the x, y, and z directions, respectively, acting on the four nodes at the free end. (

**d**) The variation of periodic force.

**Figure 3.**Numerical simulation results of the NF of the Miura tube. (

**a**) NNF variation with wall thickness of the Miura tube (

**b**). NNF variation with side length ratio of the Miura tube. (

**c**) NNF variation with folding angle of the Miura tube.

**Figure 5.**DDR of the Miura tube with different thicknesses t(θ = 130°, a/b = 1) (

**a**) x-displacement of the Miura tube under force along the x-direction, (

**b**) y-displacement of the Miura tube under force along the y-direction, and (

**c**) z-displacement of the Miura tube under force along the z-direction.

**Figure 6.**DDR of the Miura tube when folding angle θ varies(t = 0.6 mm, a/b = 1) (

**a**) x-displacement of the Miura tube under force along the x-direction, (

**b**) y-displacement of the Miura tube under force along the y-direction, and (

**c**) z-displacement of the Miura tube under force along the z-direction.

**Figure 7.**DDR of the Miura tube for different side length ratios of parallelogram a/b(θ = 130°, t = 0.6 mm) (

**a**) x-displacement of the Miura tube under force along the x-direction, (

**b**) y-displacement of the Miura tube under force along the y-direction, and (

**c**) z-displacement of the Miura tube under force along the z-direction.

**Figure 8.**Numerical simulation results of the NNF of the Miura tube when the number of arrangements of Miura sheet units varied.

**Figure 9.**DDR of the Miura tube when the number of arrangements of Miura sheet units varied (

**a**) x-displacement of the Miura tube under force along the x-direction, (

**b**) y-displacement of the Miura tube under force along the y-direction, and (

**c**) z-displacement of the Miura tube under force along the z-direction.

Material Properties | Values | |
---|---|---|

Young’s modulus/GPa | E_{1} | 121 |

E_{2} | 8.6 | |

E_{3} | 8.6 | |

Shear modulus/GPa | G_{12} | 4.7 |

G_{13} | 4.7 | |

G_{23} | 3.1 | |

Poisson’s ratio | v | 0.27 |

density/(kg·m^{−3}) | ρ | 1490 |

Fixed Parameters | Changeable Parameters | NF | ||
---|---|---|---|---|

ω_{1}/Hz | ω_{2}/Hz | ω_{3}/Hz | ||

a = 10 mm, a/b = 1 θ = 130°, β = 55° ϕ = 0° | t = 0.2 mm | 616 | 1084 | 2785 |

t = 0.4 mm | 804 | 1264 | 4277 | |

t = 0.6 mm | 956 | 1398 | 4677 | |

t = 0.8 mm | 1080 | 1507 | 4745 | |

a = 10 mm, t = 0.6 mm θ = 130°, β = 55° ϕ = 0° | a/b = 1 | 956 | 1398 | 4677 |

a/b = 1.4 | 1914 | 2709 | 6956 | |

a/b = 1.8 | 3205 | 4528 | 8759 | |

a/b = 2.2 | 4705 | 6695 | 8647 | |

a = 10 mm, a/b = 1 t = 0.6 mm, β = 55° ϕ = 0° | θ = 50° | 717 | 1135 | 2443 |

θ = 70° | 712 | 1019 | 2804 | |

θ = 90° | 821 | 982 | 3390 | |

θ = 110° | 974 | 1046 | 4359 | |

θ = 130° | 956 | 1398 | 4677 |

Group | Layout Scheme | NNF | ||
---|---|---|---|---|

ω_{1}/Hz | ω_{2}/Hz | ω_{3}/Hz | ||

1 | 0°/0°/0° | 956 | 1398 | 4677 |

2 | 90°/90°/90° | 647 | 1027 | 3608 |

3 | 0°/90°/0° | 1052 | 1572 | 5134 |

4 | 90°/0°/90° | 899 | 1473 | 4766 |

5 | 0°/45°/0° | 1006 | 1580 | 5489 |

6 | 0°/−45°/0° | 1002 | 1539 | 5315 |

7 | 45°/0°/−45° | 728 | 1322 | 4008 |

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**MDPI and ACS Style**

Zhu, H.; Li, Z.; Wang, R.; Chen, S.; Zhang, C.; Li, F.
Revealing the Dynamic Characteristics of Composite Material-Based Miura-Origami Tube. *Materials* **2021**, *14*, 6374.
https://doi.org/10.3390/ma14216374

**AMA Style**

Zhu H, Li Z, Wang R, Chen S, Zhang C, Li F.
Revealing the Dynamic Characteristics of Composite Material-Based Miura-Origami Tube. *Materials*. 2021; 14(21):6374.
https://doi.org/10.3390/ma14216374

**Chicago/Turabian Style**

Zhu, Houyao, Zhixin Li, Ruikun Wang, Shouyan Chen, Chunliang Zhang, and Fangyi Li.
2021. "Revealing the Dynamic Characteristics of Composite Material-Based Miura-Origami Tube" *Materials* 14, no. 21: 6374.
https://doi.org/10.3390/ma14216374