# 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

- European Safety Agency. Certification Specification and Acceptable Means of Compliance and Guidance Material for Aircraft Noise CS-36; European Safety Agency: Cologne, Germany, 2016. [Google Scholar]
- Kurzke, J. Fundamental Differences Between Conventional and Geared Turbofans. In Volume 1: Aircraft Engine; Ceramics; Coal, Biomass and Alternative Fuels; Controls, Diagnostics and Instrumentation; Education; Electric Power; Awards and Honors; ASME Turbo Expo: Orlando, FL, USA, 2009; pp. 145–153. ISBN 978-0-7918-4882-1. [Google Scholar]
- Carolus, T.; Schneider, M.; Reese, H. Axial flow fan broad-band noise and prediction. J. Sound Vib.
**2007**, 300, 50–70. [Google Scholar] [CrossRef] - Rolls-Royce Public Limited Company. The Jet Engine, 6th ed.; John Wiley & Sons Ltd. on Behalf of Rolls-Royce Plc: Chichester, UK, 2015; ISBN 9781119065999. [Google Scholar]
- Li, L.; Liu, Y.; Zhang, F.; Sun, Z. Several explanations on the theoretical formula of Helmholtz resonator. Adv. Eng. Softw.
**2017**, 114, 361–371. [Google Scholar] [CrossRef] - Sugimoto, R.; Murray, P.; Astley, R.J. Folded Cavity Liners for Turbofan Engine Intakes. In Proceedings of the 18th AIAA/CEAS Aeroacoustics Conference (33rd AIAA Aeroacoustics Conference), Colorado Springs, CO, USA, 4–6 June 2012; American Institute of Aeronautics and Astronautics: Reston, VA, USA, 2012; p. 06042012, ISBN 978-1-60086-932-7. [Google Scholar]
- Hoeschler, K.; Sarradj, E.; Modler, N.; Enghardt, L. Novel Jet Engine Acoustic Liner with improved Broadband Noise Absorption. In Proceedings of the 31st Congress of the International Council of the Aeronautical Sciences, Belo Horizonte, Brazil, 9–14 September 2018. [Google Scholar]
- Dannemann, M.; Kucher, M.; Kunze, E.; Modler, N.; Knobloch, K.; Enghardt, L.; Sarradj, E.; Höschler, K. Experimental Study of Advanced Helmholtz Resonator Liners with Increased Acoustic Performance by Utilising Material Damping Effects. Appl. Sci.
**2018**, 8, 1923. [Google Scholar] [CrossRef][Green Version] - Knobloch, K.; Enghardt, L.; Bake, F. Helmholtz Resonator Liner with Flexible Walls. In Proceedings of the 2018 AIAA/CEAS Aeroacoustics Conference, Atlanta, GA, USA, 25–29 June 2018; American Institute of Aeronautics and Astronautics: Reston, VA, USA; p. 06252018, ISBN 978-1-62410-560-9. [Google Scholar]
- Neubauer, M.; Dannemann, M.; Herzer, N.; Schwarz, B.; Modler, N. Analysis of a Film Forming Process through Coupled Image Correlation and Infrared Thermography. Polymers
**2022**, 14, 1231. [Google Scholar] [CrossRef] [PubMed] - Read, B.E.; Dean, G.D. The Determination of Dynamic Properties of Polymers and Composites, 1st ed.; Wiley: New York, NY, USA, 1978; ISBN 0-470-26543-4. [Google Scholar]
- Menard, K.P.; Menard, N.R. Dynamic Mechanical Analysis, 3rd ed.; CRC Press: Boca Raton, FL, USA, 2020; ISBN 9780429190308. [Google Scholar]
- Govorčin Bajsić, E.; Rek, V.; Ćosić, I. Preparation and Characterization of Talc Filled Thermoplastic Polyurethane/Polypropylene Blends. J. Polym.
**2014**, 2014, 1–8. [Google Scholar] [CrossRef][Green Version] - Strankowski, M.; Korzeniewski, P.; Strankowska, J.; S, A.A.; Thomas, S. Morphology, Mechanical and Thermal Properties of Thermoplastic Polyurethane Containing Reduced Graphene Oxide and Graphene Nanoplatelets. Materials
**2018**, 11, 82. [Google Scholar] [CrossRef] [PubMed][Green Version] - Zhang, D.; He, M.; Qin, S.; Yu, J.; Guo, J.; Xu, G. Study on dynamic mechanical, thermal, and mechanical properties of long glass fiber reinforced thermoplastic polyurethane/poly(butylene terephthalate) composites. Polym. Compos.
**2018**, 39, 63–72. [Google Scholar] [CrossRef] - Salem, T.F.; Tirkes, S.; Akar, A.O.; Tayfun, U. Enhancement of mechanical, thermal and water uptake performance of TPU/jute fiber green composites via chemical treatments on fiber surface. e-Polymers
**2020**, 20, 133–143. [Google Scholar] [CrossRef][Green Version] - Beloshenko, V.; Beygelzimer, Y.; Chishko, V.; Savchenko, B.; Sova, N.; Verbylo, D.; Voznyak, A.; Vozniak, I. Mechanical Properties of Flexible TPU-Based 3D Printed Lattice Structures: Role of Lattice Cut Direction and Architecture. Polymers
**2021**, 13, 2986. [Google Scholar] [CrossRef] [PubMed] - Neubauer, M.; Schwaericke, F.; Radmann, V.; Sarradj, E.; Modler, N.; Dannemann, M. Material Selection Process for Acoustic and Vibration Applications Using the Example of a Plate Resonator. Materials
**2022**, 15, 2935. [Google Scholar] [CrossRef] [PubMed] - Williams, M.L.; Landel, R.F.; Ferry, J.D. The Temperature Dependence of Relaxation Mechanisms in Amorphous Polymers and Other Glass-forming Liquids. J. Am. Chem. Soc.
**1955**, 77, 3701–3707. [Google Scholar] [CrossRef] - Chae, S.-H.; Zhao, J.-H.; Edwards, D.R.; Ho, P.S. Characterization of the Viscoelasticity of Molding Compounds in the Time Domain. J. Electron. Mater.
**2010**, 39, 419–425. [Google Scholar] [CrossRef] - Trivedi, A.R.; Siviour, C.R. A novel methodology for predicting the high rate mechanical response of polymers from low rate data: Application to (plasticised) poly(vinyl chloride). Mech. Time-Depend Mater.
**2021**, 25, 383–409. [Google Scholar] [CrossRef] - Lakes, R.S. Viscoelastic Materials; Cambridge University Press: Cambridge, UK, 2009; ISBN 978-0-521-88568-3. [Google Scholar]
- Nasdala, L. FEM-Formelsammlung Statik und Dynamik: Hintergrundinformationen, Tipps und Tricks, 1st ed.; Vieweg+Teubner Verlag/Springer Fachmedien Wiesbaden GmbH Wiesbaden: Wiesbaden, Germany, 2010. [Google Scholar]
- Schiessel, H.; Metzler, R.; Blumen, A.; Nonnenmacher, T.F. Generalized viscoelastic models: Their fractional equations with solutions. J. Phys. A: Math. Gen.
**1995**, 28, 6567–6584. [Google Scholar] [CrossRef] - Koeller, R.C. Applications of Fractional Calculus to the Theory of Viscoelasticity. J. Appl. Mech.
**1984**, 51, 299–307. [Google Scholar] [CrossRef] - Mainardi, F.; Gorenflo, R. Time-fractional derivatives in relaxation processes: A tutorial survey. Fract. Calc. Appl. Anal.
**2007**, 10, 269–308. [Google Scholar] - Monje, C.A.; Chen, Y.; Vinagre, B.M.; Xue, D.; Feliu, V. Fractional-Order Systems and Controls: Fundamentals and Applications, 1st ed.; Springer: London, UK, 2010; ISBN 978-1-84996-334-3. [Google Scholar]
- Park, S.W.; Kim, Y.R. Fitting Prony-Series Viscoelastic Models with Power-Law Presmoothing. J. Mater. Civ. Eng.
**2001**, 13, 26–32. [Google Scholar] [CrossRef] - Elastollan, N.N. Physical Properties. Available online: https://plastics-rubber.basf.com/global/assets/en/Performance_Polymers/Brochures/Elastollan/Elastollan_Properties-Physical-Properties.pdf (accessed on 27 October 2022).
- Kucher, M.; Dannemann, M.; Böhm, R.; Modler, N. An Experimental Approach for the Determination of the Mechanical Properties of Base-Excited Polymeric Specimens at Higher Frequency Modes. Vibration
**2022**, 5, 429–441. [Google Scholar] [CrossRef] - Capps, R.N. Dynamic Young’s moduli of some commercially available polyurethanes. J. Acoust. Soc. Am.
**1983**, 73, 2000–2005. [Google Scholar] [CrossRef]

**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