# Experimental Study on Dynamic Properties of a Recycled Composite Sleeper and Its Theoretical Model

^{1}

^{2}

^{3}

^{*}

## Abstract

**:**

## 1. Introduction

## 2. A Test for the Dynamic Properties of Composite Sleeper

#### 2.1. Test Method and Equipment

#### 2.2. Process

#### 2.3. Test Results

## 3. Prediction of the Untested Dynamic Properties of the Composite Sleeper

#### 3.1. Time-Temperature Superposition (TTS) and Williams–Landel–Ferry (WLF) Formula

_{0}, frequency f

_{0}, and density ${\rho}_{0}$ [22]. The calculations are shown in Formulas (8) and (9):

_{1}and C

_{2}are constants, which are related to the reference temperature and material type.

_{0}can be calculated by the following formula:

^{−4}/k.

#### 3.2. Predicted Results

## 4. Modeling Frequency-Dependent Composite Sleeper Properties

#### 4.1. Generalized Maxwell Model

#### 4.2. Model Characterization Results

## 5. Discussion

## 6. Conclusions

## Author Contributions

## Funding

## Acknowledgments

## Conflicts of Interest

## References

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**Figure 2.**Stress/strain time history curve: (

**a**) Ideal elastic materials, (

**b**) viscoelastic materials, (

**c**) ideal viscous materials.

**Figure 5.**A set of viscoelastic parameters of recycled composite sleepers: (

**a**) Complex modulus, (

**b**) storage modulus, (

**c**) loss modulus, (

**d**) loss factor.

**Figure 6.**Viscoelastic parameters of three groups of recycled composite sleepers at 15 °C: (

**a**) Complex modulus, (

**b**) storage modulus, (

**c**) loss modulus, (

**d**) loss factor.

**Figure 7.**Master curve of viscoelastic parameters of the composite sleeper at 15 °C: (

**a**) Complex modulus, (

**b**) storage modulus, (

**c**) loss modulus, (

**d**) loss factor.

**Figure 8.**Common models: (

**a**) Maxwell model, (

**b**) Kelvin–Voigt model, (

**c**) Burgers model, (

**d**) generalized Maxwell model.

**Figure 9.**Fitting curve of viscoelastic parameters of composite sleeper at 15 °C: (

**a**) Complex modulus, (

**b**) storage modulus, (

**c**) loss modulus, (

**d**) loss factor.

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

${E}_{\infty}$/MPa | 1722 |

${E}_{1}$/MPa | 626 |

${\tau}_{1}$/s | 0.012 |

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

${E}_{\infty}$/MPa | 1450 |

${E}_{1}$/MPa | 299 |

${\tau}_{1}$/s | 1 |

${E}_{2}$/MPa | 188 |

${\tau}_{2}$/s | 0.1 |

${E}_{3}$/MPa | 189 |

${\tau}_{3}$/s | 0.01 |

${E}_{4}$/MPa | 315 |

${\tau}_{4}$/s | 0.001 |

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**MDPI and ACS Style**

Zhao, Z.; Gao, Y.; Li, C.
Experimental Study on Dynamic Properties of a Recycled Composite Sleeper and Its Theoretical Model. *Symmetry* **2021**, *13*, 17.
https://doi.org/10.3390/sym13010017

**AMA Style**

Zhao Z, Gao Y, Li C.
Experimental Study on Dynamic Properties of a Recycled Composite Sleeper and Its Theoretical Model. *Symmetry*. 2021; 13(1):17.
https://doi.org/10.3390/sym13010017

**Chicago/Turabian Style**

Zhao, Zhenhang, Ying Gao, and Chenghui Li.
2021. "Experimental Study on Dynamic Properties of a Recycled Composite Sleeper and Its Theoretical Model" *Symmetry* 13, no. 1: 17.
https://doi.org/10.3390/sym13010017