# DMA of TPU Films and the Modelling of Their Viscoelastic Properties for Noise Reduction in Jet Engines

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## Abstract

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## 1. Introduction

## 2. Materials and Methods

#### 2.1. Material

#### 2.2. Experimental Apparatus and Procedure

#### 2.3. Viscoelastic Material Modelling

## 3. Results and Discussion

#### 3.1. Analysys of Production-Related Material Orthotropy

#### 3.2. Frequency Dependent Complex Modulus

#### 3.3. Identified Viscoelastic Material Parameter

#### 3.4. Effect of Flight Cycle Conditions on Mechanical Properties

## 4. Conclusions

## Author Contributions

## Funding

## Institutional Review Board Statement

## Informed Consent Statement

## Data Availability Statement

## Conflicts of Interest

## References

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**Figure 1.**(

**a**) Experimental setup of the DMA test in tensile mode, (

**b**) schematic representation of the orthogonal and parallel removal of the film specimen with respect to the manufacturing direction of the film material.

**Figure 2.**Schematic representation of used rheological models: (

**a**) generalized Maxwell model, (

**b**) fractional four-parameter model.

**Figure 4.**Averaged values for storage modulus ${E}^{\prime}$, loss modulus ${E}^{\prime \prime}$ and mechanical loss factor $\mathrm{tan}\mathsf{\delta}$ at the frequencies of $f$ = 0.1, 0.3, 0.5, 1, 2, 3, 5, 10, 30, 50 Hz.

**Figure 5.**Calculated shift factor as a function of temperature based on the WLF method and an eighth-degree polynomial approximation.

**Figure 6.**Master curves generated by shifting ${E}^{\prime}$ and ${E}^{\prime \prime}$ using the TTS principle with respect to a reference temperature of 20 °C: (

**a**) using an eighth-degree polynomial approximation and (

**b**) the WLF shift factors.

**Figure 7.**Approximated storage and loss modulus using generalized Maxwell models and a fractional model: (

**a**) Prony series without pre-smoothing, (

**b**) Prony series with pre-smoothing.

**Figure 8.**Resulting relaxation moduli of Prony-series of the generalized Maxwell model without and with pre-smoothing.

**Figure 9.**(

**a**) Schematic flight cycle with a typical temperature curve; (

**b**) Change of the mechanical loss factor in dependency of standard sinusoidal vibration test’s excitation frequency (compare RTCA DO-160G).

Temperature [°C] | ${\mathit{E}}^{\prime}\left[\mathit{M}\mathit{P}\mathit{a}\right]$ | ||||||
---|---|---|---|---|---|---|---|

Specimen 1 Parallel | Specimen 2 Parallel | Specimen 3P arallel | Specimen 4 Orthogonal | Specimen 5 Orthogonal | Specimen 6 Orthogonal | Relative Standard Deviation [%] | |

−60 | 1032.22 | 1009.03 | 937.32 | 1063.32 | 899.23 | 941.61 | 5.94 |

−40 | 118.79 | 121.74 | 112.63 | 131.49 | 111.11 | 109.92 | 6.37 |

−20 | 28.10 | 29.06 | 27.22 | 31.07 | 28.11 | 26.83 | 4.90 |

0 | 17.17 | 18.40 | 16.76 | 19.75 | 17.96 | 17.17 | 5.61 |

20 | 14.41 | 15.79 | 14.24 | 17.07 | 15.55 | 15.08 | 6.17 |

40 | 13.68 | 14.40 | 13.54 | 15.28 | 14.23 | 14.19 | 3.97 |

60 | 10.81 | 11.44 | 10.70 | 12.30 | 11.41 | 11.33 | 4.61 |

80 | 6.98 | 8.93 | 8.26 | 9.43 | 8.51 | 8.41 | 8.92 |

100 | 0.00 | 6.44 | 5.98 | 6.55 | 5.56 | 4.74 | 11.25 |

$\mathit{n}$ | 3 | 7 | 10 | 12 |
---|---|---|---|---|

Without pre-smoothing | ||||

Error measure $r$ | 0.294 | 0.111 | 0.109 | 0.109 |

With pre-smoothing | ||||

Error measure $r$ | 0.298 | 0.124 | 0.122 | 0.122 |

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**MDPI and ACS Style**

Neubauer, M.; Pohl, M.; Kucher, M.; Böhm, R.; Höschler, K.; Modler, N.
DMA of TPU Films and the Modelling of Their Viscoelastic Properties for Noise Reduction in Jet Engines. *Polymers* **2022**, *14*, 5285.
https://doi.org/10.3390/polym14235285

**AMA Style**

Neubauer M, Pohl M, Kucher M, Böhm R, Höschler K, Modler N.
DMA of TPU Films and the Modelling of Their Viscoelastic Properties for Noise Reduction in Jet Engines. *Polymers*. 2022; 14(23):5285.
https://doi.org/10.3390/polym14235285

**Chicago/Turabian Style**

Neubauer, Moritz, Michael Pohl, Michael Kucher, Robert Böhm, Klaus Höschler, and Niels Modler.
2022. "DMA of TPU Films and the Modelling of Their Viscoelastic Properties for Noise Reduction in Jet Engines" *Polymers* 14, no. 23: 5285.
https://doi.org/10.3390/polym14235285