# Modal Parameters Evaluation in a Full-Scale Aircraft Demonstrator under Different Environmental Conditions Using HS 3D-DIC

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## Abstract

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## 1. Introduction

## 2. Three-Dimensional Digital Image Correlation

- Specimen and set-up preparation. The specimen must exhibit a random speckle distribution on its surface. Normally, it is coated with white paint and, subsequently, a random artificial speckle pattern is generated by spraying black paint over the white paint [39].
- Calibration of the stereoscopy system. The calibration of the cameras is performed by placing a calibration plate with a printed grid on it in the test space, where the specimen is located during the experiment. Thus, it is possible to establish a correspondence with the local coordinate system of each camera and calibration parameters (Figure 4) [10,40,41,42].
- Images capture. As was indicated above, a perfect synchronization of the cameras’ recording is necessary to correctly process the results. This is achieved by synchronizing the internal camera’s clock and simultaneous triggering.
- Image processing. Images were processed to obtain the measured displacement and strain fields.

## 3. Materials and Method

#### 3.1. Tests on Specimen 1

#### 3.2. Tests on Specimen 2

#### 3.3. Test for Full-Field Measurement Using HS 3D-DIC

#### 3.4. Image Decomposition Comparison

_{k}(i,j) to decompose displacement contours I(i,j) into a set of coefficients or shape descriptors, s

_{k}, with the same units as the original sets of data.

## 4. Results and Discussion

#### 4.1. Specimen 1 under Differential Pressure

#### 4.2. Specimen 2

## 5. Conclusions

## Acknowledgments

## Author Contributions

## Conflicts of Interest

## References

- Wright, R.I.; Kidner, M.R.F. Vibration Absorbers: A Review of Applications in Interior Noise Control of Propeller Aircraft. J. Vib. Control
**2004**, 10, 1221–1237. [Google Scholar] [CrossRef] - Haase, T.; Unruh, O.; Algermissen, S.; Pohl, M. Active control of counter-rotating open rotor interior noise in a Dornier 728 experimental aircraft. J. Sound Vib.
**2016**, 376, 18–32. [Google Scholar] [CrossRef] - Yan, Y.; Li, P.; Lin, H. Analysis and experimental validation of the middle-frequency vibro-acoustic coupling property for aircraft structural model based on the wave coupling hybrid FE-SEA method. J. Sound Vib.
**2016**, 371, 227–236. [Google Scholar] [CrossRef] - Ewins, D.J. Modal Testing: Theory, Practice, and Application, 2nd ed.; Roberts, J.B., Ed.; Research Studies Press LTD: Baldock, UK, 2000; ISBN 978-0863802188. [Google Scholar]
- Stanbridge, A.B.; Ewins, D.J. Modal testing using a scanning laser doppler vibrometer. Mech. Syst. Signal Process.
**1999**, 13, 255–270. [Google Scholar] [CrossRef] - Stanbridge, A.B.; Martarelli, M.; Ewins, D.J. Measuring area vibration mode shapes with a continuous-scan LDV. Meas. J. Int. Meas. Confed.
**2004**, 35, 181–189. [Google Scholar] [CrossRef] - O’Malley, P.; Woods, T.; Judge, J.; Vignola, J. Five-axis scanning laser vibrometry for three-dimensional measurements of non-planar surfaces. Meas. Sci. Technol.
**2009**, 20, 115901. [Google Scholar] [CrossRef] - Bertini, L.; Monelli, B.; Neri, P.; Santus, C.; Guglielmo, A. Robot Assisted Modal Analysis on a Stationary Bladed Wheel. In Dynamics, Vibration and Control; Energy; Fluids Engineering; Micro and Nano Manufacturing; ASME: Copenhagen, Denmark, 2014; Volume 2, p. V002T07A033. [Google Scholar]
- Bertini, L.; Neri, P.; Santus, C.; Guglielmo, A. Automated Experimental Modal Analysis of Bladed Wheels with an Anthropomorphic Robotic Station. Exp. Mech.
**2017**, 57, 273–285. [Google Scholar] [CrossRef] - Schreier, H.; Orteu, J.-J.; Sutton, M.A. Image Correlation for Shape, Motion and Deformation Measurements; Springer: Boston, MA, USA, 2009; ISBN 978-0-387-78746-6. [Google Scholar]
- Helfrick, M.N.; Niezrecki, C.; Avitabile, P.; Schmidt, T. 3D digital image correlation methods for full-field vibration measurement. Mech. Syst. Signal Process.
**2010**, 25, 917–927. [Google Scholar] [CrossRef] - Warren, C.; Niezrecki, C.; Avitabile, P.; Pingle, P. Comparison of FRF measurements and mode shapes determined using optically image based, laser, and accelerometer measurements. Mech. Syst. Signal Process.
**2011**, 25, 2191–2202. [Google Scholar] [CrossRef] - Reu, P.L.; Rohe, D.P.; Jacobs, L.D. Comparison of DIC and LDV for practical vibration and modal measurements. Mech. Syst. Signal Process.
**2017**, 86, 2–16. [Google Scholar] [CrossRef] - Ha, N.S.; Jin, T.; Goo, N.S. Modal analysis of an artificial wing mimicking an Allomyrina dichotoma beetle’s hind wing for flapping-wing micro air vehicles by noncontact measurement techniques. Opt. Lasers Eng.
**2013**, 51, 560–570. [Google Scholar] [CrossRef] - Baqersad, J.; Carr, J.; Lundstrom, T.; Niezrecki, C.; Avitabile, P.; Slattery, M. Dynamic characteristics of a wind turbine blade using 3D digital image correlation. In Proceedings of SPIE; Kundu, T., Ed.; SPIE: Bellingham, WA, USA, 2012; Volume 8348, p. 83482I. [Google Scholar]
- Siebert, T.; Becker, T.; Spiltthof, K.; Neumann, I.; Krupka, R. High-speed digital image correlation: Error estimations and applications. Opt. Eng.
**2007**, 46, 51004. [Google Scholar] [CrossRef] - Wang, W.; Mottershead, J.E.; Ihle, A.; Siebert, T.; Reinhard Schubach, H. Finite element model updating from full-field vibration measurement using digital image correlation. J. Sound Vib.
**2011**, 330, 1599–1620. [Google Scholar] [CrossRef] - Felipe-Sesé, L.; Díaz, F.A. Damage methodology approach on a composite panel based on a combination of Fringe Projection and 2D Digital Image Correlation. Mech. Syst. Signal Process.
**2018**, 101, 467–479. [Google Scholar] [CrossRef] - Siebert, T.; Wood, R.; Splitthof, K. High speed image correlation for vibration analysis. J. Phys. Conf. Ser.
**2009**, 181, 12064. [Google Scholar] [CrossRef] - Ehrhardt, D.A.; Allen, M.S.; Yang, S.; Beberniss, T.J. Full-field linear and nonlinear measurements using Continuous-Scan Laser Doppler Vibrometry and high speed Three-Dimensional Digital Image Correlation. Mech. Syst. Signal Process.
**2017**, 86, 82–97. [Google Scholar] [CrossRef] - Molina-Viedma, A.J.; Felipe-Sesé, L.; López-Alba, E.; Díaz, F. High frequency mode shapes characterisation using Digital Image Correlation and phase-based motion magnification. Mech. Syst. Signal Process.
**2018**, 102, 245–261. [Google Scholar] [CrossRef] - Berke, R.B.; Sebastian, C.M.; Chona, R.; Patterson, E.A.; Lambros, J. High Temperature Vibratory Response of Hastelloy-X: Stereo-DIC Measurements and Image Decomposition Analysis. Exp. Mech.
**2015**, 56, 231–243. [Google Scholar] [CrossRef] - Barone, S.; Neri, P.; Paoli, A.; Razionale, A. Digital Image Correlation Based on Projected Pattern for High Frequency Vibration Measurements. Procedia Manuf.
**2017**, 11, 1592–1599. [Google Scholar] [CrossRef] - Trebuňa, F.; Hagara, M. Experimental modal analysis performed by high-speed digital image correlation system. Measurement
**2014**, 50, 78–85. [Google Scholar] [CrossRef] - Wang, W.; Mottershead, J.E.; Siebert, T.; Pipino, A. Frequency response functions of shape features from full-field vibration measurements using digital image correlation. Mech. Syst. Signal Process.
**2012**, 28, 333–347. [Google Scholar] [CrossRef] - Beberniss, T.J.; Ehrhardt, D.A. High-speed 3D digital image correlation vibration measurement: Recent advancements and noted limitations. Mech. Syst. Signal Process.
**2017**, 86, 35–48. [Google Scholar] [CrossRef] - Molina-Viedma, Á.J.; López-Alba, E.; Felipe-Sesé, L.; Díaz, F.A. Full-field modal analysis during base motion excitation using high-speed 3D digital image correlation. Meas. Sci. Technol.
**2017**, 28, 105402. [Google Scholar] [CrossRef] - Ha, N.S.; Vang, H.M.; Goo, N.S. Modal Analysis Using Digital Image Correlation Technique: An Application to Artificial Wing Mimicking Beetle’s Hind Wing. Exp. Mech.
**2015**, 989–998. [Google Scholar] [CrossRef] - Rizo-Patron, S.; Sirohi, J. Operational Modal Analysis of a Helicopter Rotor Blade Using Digital Image Correlation. Exp. Mech.
**2017**, 57, 367–375. [Google Scholar] [CrossRef] - Huňady, R.; Hagara, M. A new procedure of modal parameter estimation for high-speed digital image correlation. Mech. Syst. Signal Process.
**2017**, 93, 66–79. [Google Scholar] [CrossRef] - Yu, L.; Pan, B. Single-camera high-speed stereo-digital image correlation for full-field vibration measurement. Mech. Syst. Signal Process.
**2017**, 94, 374–383. [Google Scholar] [CrossRef] - Wang, W.; Mottershead, J.E.; Mares, C. Vibration mode shape recognition using image processing. J. Sound Vib.
**2009**, 326, 909–938. [Google Scholar] [CrossRef] - Wang, W.; Mottershead, J.E.; Mares, C. Mode-shape recognition and finite element model updating using the Zernike moment descriptor. Mech. Syst. Signal Process.
**2009**, 23, 2088–2112. [Google Scholar] [CrossRef] - Validation of Numerical Engineering Simulations: Standardisation Actions (VANESSA). European FP7 Project Grant Agreement No. NMP3-SA-2012-319116. Available online: http://www.engineeringvalidation.org/ (accessed on 1 November 2017).
- Lampeas, G.; Pasialis, V.; Lin, X.; Patterson, E.A. On the validation of solid mechanics models using optical measurements and data decomposition. Simul. Model. Pract. Theory
**2015**, 52, 92–107. [Google Scholar] [CrossRef] - Wang, W.; Mottershead, J.E.; Sebastian, C.M.; Patterson, E.A. Shape features and finite element model updating from full-field strain data. Int. J. Solids Struct.
**2011**, 48, 1644–1657. [Google Scholar] [CrossRef] - Sebastian, C.; Hack, E.; Patterson, E. An approach to the validation of computational solid mechanics models for strain analysis. J. Strain Anal. Eng. Des.
**2013**, 48, 36–47. [Google Scholar] [CrossRef] - Molina-Viedma, A.; López-Alba, E.; Felipe-Sesé, L.; Díaz, F.; Rodríguez-Ahlquist, J.; Iglesias-Vallejo, M. A non-invasive methodology for modal characterisation of an aircraft cabin using high speed 3D digital image correlation. In Proceedings of the 24th International Congress on Sound and Vibration (ICSV 2017), London, UK, 23–27 July 2017. [Google Scholar]
- Lecompte, D.; Smits, A.; Bossuyt, S.; Sol, H.; Vantomme, J.; Van Hemelrijck, D.; Habraken, A.M. Quality assessment of speckle patterns for digital image correlation. Opt. Lasers Eng.
**2006**, 44, 1132–1145. [Google Scholar] [CrossRef] - Sutton, M.A.; Yan, J.H.; Tiwari, V.; Schreier, H.W.; Orteu, J.J. The effect of out-of-plane motion on 2D and 3D digital image correlation measurements. Opt. Lasers Eng.
**2008**, 46, 746–757. [Google Scholar] [CrossRef] - Chen, F.; Chen, X.; Xie, X.; Feng, X.; Yang, L. Full-field 3D measurement using multi-camera digital image correlation system. Opt. Lasers Eng.
**2013**, 51, 1044–1052. [Google Scholar] [CrossRef] - Tang, Z.; Liang, J.; Xiao, Z.; Guo, C. Large deformation measurement scheme for 3D digital image correlation method. Opt. Lasers Eng.
**2012**, 50, 122–130. [Google Scholar] [CrossRef] - Rao, K.R.; Kim, D.N.; Hwang, J.J. Fast Fourier Transform—Algorithms and Applications; Signals and Communication Technology; Springer: Dordrecht, The Netherlands, 2010; ISBN 978-1-4020-6628-3. [Google Scholar]

**Figure 1.**Clean Sky/Green Regional Aircraft MT2 cockpit demonstrator (

**a**) and test rig (

**b**) developed by Airbus Defence and Space.

**Figure 5.**Set-up for impact hammer tests on the passenger window of the GRA front fuselage demonstrator (exterior view).

**Figure 9.**(

**a**) Optical system on the supporting bar; (

**b**) supporting bar attachment to the bulkhead; and (

**c**) model of the global cockpit demonstrator configuration.

**Figure 10.**Images of the window from the cameras point of view. (

**a**) Left-hand camera; and (

**b**) right-hand camera. Dotted lines represent the area analyzed using shape descriptor image decomposition; (

**c**) sample of the facets grid.

**Figure 11.**Evolution of the correlation coefficient between original and reconstructed displacement contours of specimen 1 as a function of the shape descriptors employed.

**Figure 13.**Normalized operational deflection shapes in the out-of-plane direction obtained using HS 3D-DIC under different excitation configurations.

**Figure 14.**Additional normalized ODSs in the out-of-plane direction detected using HS 3D-DIC and random excitation.

**Figure 16.**Normalized ODSs in the out-of-plane direction obtained using HS 3D-DIC in a random excitation test under differential pressure.

**Figure 17.**Reconstruction of the percentage differences between shape descriptors representing both ODSs in non-pressurized and pressurized states. (

**a**) Mode 1; (

**b**) Mode 2; (

**c**) Mode 3; and (

**d**) Mode 4.

**Figure 18.**Operational deflection shapes of the second window specimen obtained using HS 3D-DIC in a sine test.

Excitation | Sensor | Specimens | Environment | Results |
---|---|---|---|---|

Impact | Accelerometers | 1 and 2 | Ambient | Natural frequencies |

Sine | HS 3D-DIC | 1 and 2 | Ambient | ODSs |

Random | HS 3D-DIC | 1 | Ambient and differential pressure | Natural frequencies and ODSs |

Mode Denomination | Non-Pressurized (Hz) | Differential Pressure (Hz) |
---|---|---|

1 | 124 | 148 |

2 | 155 | 196 |

3 | 215 | 252 |

4 | 267 | 276 |

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**MDPI and ACS Style**

Molina-Viedma, Á.J.; López-Alba, E.; Felipe-Sesé, L.; Díaz, F.A.; Rodríguez-Ahlquist, J.; Iglesias-Vallejo, M.
Modal Parameters Evaluation in a Full-Scale Aircraft Demonstrator under Different Environmental Conditions Using HS 3D-DIC. *Materials* **2018**, *11*, 230.
https://doi.org/10.3390/ma11020230

**AMA Style**

Molina-Viedma ÁJ, López-Alba E, Felipe-Sesé L, Díaz FA, Rodríguez-Ahlquist J, Iglesias-Vallejo M.
Modal Parameters Evaluation in a Full-Scale Aircraft Demonstrator under Different Environmental Conditions Using HS 3D-DIC. *Materials*. 2018; 11(2):230.
https://doi.org/10.3390/ma11020230

**Chicago/Turabian Style**

Molina-Viedma, Ángel Jesús, Elías López-Alba, Luis Felipe-Sesé, Francisco A. Díaz, Javier Rodríguez-Ahlquist, and Manuel Iglesias-Vallejo.
2018. "Modal Parameters Evaluation in a Full-Scale Aircraft Demonstrator under Different Environmental Conditions Using HS 3D-DIC" *Materials* 11, no. 2: 230.
https://doi.org/10.3390/ma11020230