Skip to main content
SpringerLink
Log in

In-plane Operating Deflection Shape Measurement of an Aluminum Plate Using a Three-dimensional Continuously Scanning Laser Doppler Vibrometer System

  • Research paper
  • Published:
Experimental Mechanics Aims and scope Submit manuscript

Abstract

Background

In-plane vibration is significant to a structure and has been accurately solved by many numerical methods; however, there are still not enough studies on its experimental measurement.

Objective

This work aims to propose a non-contact and fast way to measure dense full-field in-plane vibration of a plate structure, which has high frequencies and low response magnitudes.

Methods

A novel three-dimensional (3D) continuously scanning laser Doppler vibrometer (CSLDV) system that contains three CSLDVs is developed to conduct full-field scanning of a plate with free boundary conditions under sinusoidal excitation to measure its 3D vibrations. Calibration among the three CSLDVs in the 3D CSLDV system based on the geometrical model of its scan mirrors is conducted to adjust their rotational angles to ensure that three laser spots can continuously and synchronously move along the same two-dimensional scan trajectory on the plate. The demodulation method is used to process the measured response to obtain in-plane operating deflection shapes (ODSs) of the plate.

Results

Four in-plane ODSs are obtained in the frequency range of 0–5000 Hz. Modal assurance criterion (MAC) values between in-plane ODSs from 3D CSLDV and step-wise scanning laser Doppler vibrometer (SLDV) measurements are larger than 95%. MAC values between ODSs from 3D CSLDV measurements and corresponding mode shapes from the finite element model of the plate are larger than 91%.

Conclusions

Results from 3D CSLDV measurements have good accuracy compared to those from SLDV measurements and numerical calculation, and the 3D CSLDV system can scan much more measurement points in much less time than the SLDV system.

This is a preview of subscription content, log in via an institution to check access.

Access this article

Log in via an institution

Price excludes VAT (USA)
Tax calculation will be finalised during checkout.

Instant access to the full article PDF.

Institutional subscriptions

Fig. 1
Fig. 2
Fig. 3
Fig. 4
Fig. 5
Fig. 6
Fig. 7
Fig. 8
Fig. 9

Similar content being viewed by others

References

  1. Chen Y, Logan P, Avitabile P, Dodson J (2019) Non-model based expansion from limited points to an augmented set of points using Chebyshev polynomials. Exp Tech 43(5):521–543

    Article  Google Scholar 

  2. Chen Y, Avitabile P, Dodson J (2020) Data consistency assessment function (DCAF). Mech Syst Signal Process 141:106688

  3. Lyon R (1986) In-plane contribution to structural noise transmission. Noise Control Engineering Journal 26:22

    Article  Google Scholar 

  4. Langley RS, Bercin AN (1994) Wave intensity analysis of high frequency vibrations. Philosophical Transactions of the Royal Society of London. Series A: Phys Eng Sci 346(1681):489–499

  5. Bercin AN (1996) An assessment of the effects of in-plane vibrations on the energy flow between coupled plates. J Sound Vib 191(5):661–680

    Article  Google Scholar 

  6. Bardell NS, Langley RS, Dunsdon JM (1996) On the free in-plane vibration of isotropic rectangular plates. J Sound Vib 191(3):459–467

    Article  Google Scholar 

  7. Wang Z, Xing Y, Sun Q (2020) Highly accurate closed-form solutions for the free in-plane vibration of rectangular plates with arbitrary homogeneous boundary conditions. J Sound Vib 470:115166

  8. Ji M, Wu Y, Ma C (2021) Analytical solutions for in-plane dominated vibrations of transversely isotropic circular plates based on high-order theories. J Sound Vib 503:116110

  9. Larsson D (1997) In-plane modal testing of a free isotropic rectangular plate. Exp Mech 37(3):339–343

    Article  Google Scholar 

  10. Batista FB, Fabro AT, Cóser LF, Arruda JRF, Albuquerque EL (2010) In-plane modal testing of a free isotropic plate using laser doppler vibrometer measurements. In AIP Conference Proceedings 1253(1):333–340. American Institute of Physics

  11. Xu YF, Zhu WD (2013) Operational modal analysis of a rectangular plate using non-contact excitation and measurement. J Sound Vib 332(20):4927–4939

    Article  Google Scholar 

  12. Miyashita T, Fujino Y (2006) Development of 3D vibration measurement system using laser doppler vibrometers. In Health Monitoring and Smart Nondestructive Evaluation of Structural and Biological Systems V 6177:61770I. International Society for Optics and Photonics

  13. Stoffregen B, Felske A (1985) Scanning laser Doppler vibration analysis system. SAE Transactions 934–940

  14. Bendel K, Fischer M, Schuessler M (2004) Vibrational analysis of power tools using a novel three-dimensional scanning vibrometer. In Sixth International Conference on Vibration Measurements by Laser Techniques: Advances and Applications 5503:177–184. International Society for Optics and Photonics

  15. Staszewski WJ, Lee BC, Traynor R (2007) Fatigue crack detection in metallic structures with Lamb waves and 3D laser vibrometry. Meas Sci Technol 18(3):727

    Article  Google Scholar 

  16. Xu W, Zhu WD, Smith SA, Cao MS (2016) Structural damage detection using slopes of longitudinal vibration shapes. J Vib Acoust 138(3):034501

  17. Rothberg SJ, Allen MS, Castellini P, Di Maio D, Dirckx JJJ, Ewins DJ, Halkon BJ, Muyshondt P, Paone N, Ryan T, Steger H (2017) An international review of laser Doppler vibrometry: Making light work of vibration measurement. Opt Lasers Eng 99:11–22

    Article  Google Scholar 

  18. Marwitz S, Zabel V (2017) An experimental evaluation of two potential improvements for 3D laser vibrometer based operational modal analysis. Exp Mech 57(8):1311–1325

    Article  Google Scholar 

  19. Chen Y, Avitabile P, Page C, Dodson J (2021) A polynomial based dynamic expansion and data consistency assessment and modification for cylindrical shell structures. Mech Syst Signal Process 154:107574

  20. Chen Y, Joffre D, Avitabile P (2018) Underwater dynamic response at limited points expanded to full-field strain response. J Vib Acoust 140(5)

  21. Yuan K, Zhu W (2021) Modeling of welded joints in a pyramidal truss sandwich panel using beam and shell finite elements. J Vib Acoust 143(4):041002

  22. Chen Y, Mendoza ASE, Griffith DT (2021) Experimental and numerical study of high-order complex curvature mode shape and mode coupling on a three-bladed wind turbine assembly. Mech Syst Signal Process 160:107873

  23. O'Malley P, Woods T, Judge J, Vignola J (2009) Five-axis scanning laser vibrometry for three-dimensional measurements of non-planar surfaces. Meas Sci Technol 20(11):115901

  24. Kim D, Song H, Khalil H, Lee J, Wang S, Park K (2014) 3-D vibration measurement using a single laser scanning vibrometer by moving to three different locations. IEEE Trans Instrum Meas 63(8):2028–2033

    Article  Google Scholar 

  25. Weekes B, Ewins D (2015) Multi-frequency, 3D ODS measurement by continuous scan laser Doppler vibrometry. Mech Syst Signal Process 58:325–339

    Article  Google Scholar 

  26. Chen DM, Zhu WD (2017) Investigation of three-dimensional vibration measurement by a single scanning laser Doppler vibrometer. J Sound Vib 387:36–52

    Article  Google Scholar 

  27. Halkon BJ, Frizzel SR, Rothberg SJ (2003) Vibration measurements using continuous scanning laser vibrometry: velocity sensitivity model experimental validation. Meas Sci Technol 14(6):773

    Article  Google Scholar 

  28. Halkon BJ, Rothberg SJ (2006) Vibration measurements using continuous scanning laser vibrometry: advanced aspects in rotor applications. Mech Syst Signal Process 20(6):1286–1299

    Article  Google Scholar 

  29. Di Maio D, Castellini P, Martarelli M, Rothberg S, Allen MS, Zhu WD, Ewins DJ (2021) Continuous scanning laser vibrometry: a raison d’être and applications to vibration measurements. Mech Syst Signal Process 156:107573

  30. Chen DM, Xu YF, Zhu WD (2017) Experimental investigation of notch-type damage identification with a curvature-based method by using a continuously scanning laser doppler vibrometer system. J Nondestr Eval 36(2):38

    Article  Google Scholar 

  31. Chen DM, Xu YF, Zhu WD (2018) Identification of damage in plates using full-field measurement with a continuously scanning laser Doppler vibrometer system. J Sound Vib 422:542–567

    Article  Google Scholar 

  32. Chen, DM, Xu, YF, Zhu, WD (2019) A comprehensive study on detection of hidden delamination damage in a composite plate using curvatures of operating deflection shapes. J Nondestr Eval 38(2):1–18

  33. Hu, Y, Guo, W, Zhu, W, Xu, Y (2019) Local damage detection of membranes based on Bayesian operational modal analysis and three-dimensional digital image correlation. Mech Syst Signal Process 131:633–648

  34. Chen DM, Zhu WD (2021) Investigation of three-dimensional vibration measurement by three scanning laser Doppler vibrometers in a continuously and synchronously scanning mode. J Sound Vib 498:115950

  35. Yuan K, Zhu WD (2021) Estimation of modal parameters of a beam under random excitation using a novel 3D continuously scanning laser Doppler vibrometer system and an extended demodulation method. Mech Syst Signal Process 155:107606

  36. Arun KS, Huang TS, Blostein SD (1987) Least-squares fitting of two 3-D point sets. IEEE Trans Pattern Anal Mach Intell 5:698–700

    Article  Google Scholar 

  37. Stanbridge AB, Ewins DJ (1999) Modal testing using a scanning laser Doppler vibrometer. Mech Syst Signal Process 13(2):255–270

    Article  Google Scholar 

  38. Ewins DJ (2000) Modal Testing: Theory, Practice, and Application, 2nd edn. Research Studies Press Ltd., Hertfordshire, UK

    Google Scholar 

Download references

Acknowledgements

The authors are grateful for the financial support from the National Science Foundation through Grant No. CMMI-1763024.

Author information

Authors and Affiliations

  1. Department of Mechanical Engineering, University of Maryland, Baltimore County, 1000 Hilltop Circle, Baltimore, MD, 21250, USA

    K. Yuan & W. D. Zhu

Authors
  1. K. Yuan
    View author publications

    You can also search for this author in PubMed Google Scholar

  2. W. D. Zhu
    View author publications

    You can also search for this author in PubMed Google Scholar

Corresponding author

Correspondence to W. D. Zhu.

Ethics declarations

Conflicts of Interest

The authors declare that there are no conflicts of interest.

Additional information

Publisher's Note

Springer Nature remains neutral with regard to jurisdictional claims in published maps and institutional affiliations.

Rights and permissions

Reprints and permissions

About this article

Check for updates. Verify currency and authenticity via CrossMark

Cite this article

Yuan, K., Zhu, W.D. In-plane Operating Deflection Shape Measurement of an Aluminum Plate Using a Three-dimensional Continuously Scanning Laser Doppler Vibrometer System. Exp Mech 62, 667–676 (2022). https://doi.org/10.1007/s11340-021-00801-x

Download citation

  • Received:

  • Accepted:

  • Published:

  • Issue Date:

  • DOI: https://doi.org/10.1007/s11340-021-00801-x

Keywords

Search

Navigation