Skip to main content
SpringerLink
Log in

A single pair-of-sensors technique for geometry consistent sensing of acceleration vector fields in beam structures: damage detection and dissipation estimation by POD modes

  • Published:
Meccanica Aims and scope Submit manuscript

Abstract

The acceleration vector field developed in a beam-like elastic structure is sampled over the space–time domain by a tri-axial accelerometer relocated over the beam surface while triggered by another mono-axial accelerometer fixed in space to attain synchronism. This technique leads to structure-geometry consistent spatio-temporal measurements of coupled structural dynamics. This result is established by extracting and interpreting the physics hidden in geometry consistent raw databases (mined by sweeping a single pair-of-sensors) with advanced proper orthogonal decomposition (POD) tools. For in-plane coupled vibrations, the dominant POD modes coincide with certain nonlinear normal modes of vibration belonging to the slow dynamics manifold structure. A parametric study reveals that they remain robust for increasing energy levels (nonlinearity) and changes in beam length-curvature (nonlinear geometry); and for out-of-plane bending and torsion vibration perturbations. Spatial local damage signatures due to a local mass and a plasticity defect are extracted from comparing logarithmically the POD modal shapes of healthy and damaged curved beams. In the presence of a local plasticity defect, certain dominant POD modes increases their internal dissipation index, the latter being modes independent for the healthy beam. This limited-sensor sensing technique is potentially useful for test and evaluation analysis of beam and cable like structural systems with complex geometries.

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
Fig. 10
Fig. 11
Fig. 12
Fig. 13
Fig. 14
Fig. 15
Fig. 16

Similar content being viewed by others

References

  1. Staszewski W, Boller C, Tomlinson G (2004) Health monitoring of aerospace structures. Wiley, Padstow

    Google Scholar 

  2. Farrar RF, Worden K (2013) Structural health monitoring: a machine learning perspective. Wiley, Chichester

    Google Scholar 

  3. Farrar RF, Worden K (2007) An introduction to structural health monitoring. Philos Trans R Soc A 365:303–315

    Article  ADS  Google Scholar 

  4. Inman DJ, Farrar CR, Lopes VLJ, Srephen VJ (eds) (2005) Damage prognosis: for aerospace, civil and mechanical systems. Wiley, Chichester

    Google Scholar 

  5. Adams A (2007) Health monitoring of structural materials and components: methods with applications. Wiley, Chichester

    Book  Google Scholar 

  6. Giurgiutiu V (2008) Structural health monitoring with piezoelectric wafer active sensors. Elsevier, Oxford

    Google Scholar 

  7. Lynch JP, Loh KJ (2006) A summary review of wireless sensors and sensor networks for structural health monitoring. Shock Vib Dig 38(2):91–128

    Article  Google Scholar 

  8. Meixner H (2003) Sensors and sensing: an engineer’s view. In: Barth F, Humphrey J, Secomb T (eds) Sensors and sensing in biology and engineering. Springer, New York

    Google Scholar 

  9. Guo H, Xiao G, Mrad N, Yao J (2011) Fiber optic sensors for structural health monitoring of air platforms. Sensors 11:3687–3705

    Article  Google Scholar 

  10. Wang G, Pran K, Sagvolden G, Havsgard GB, Jensen AE, Johnson GA, Vohra ST (2001) Ship hull structure monitoring using fibre optic sensors. Smart Mater Struct 10:472–478

    Article  ADS  Google Scholar 

  11. Lynch JP, Wang Y, Loh KJ, Yi J-H, Chung-Bang Yun C-B (2006) Performance monitoring of the Geumdang Bridge using a dense network of high-resolution wireless sensors. Smart Mater Struct 15:1561–1575

    Article  ADS  Google Scholar 

  12. Xu B, Giurgiutiu V (2007) Single mode tuning effects on lamb wave time reversal with piezoelectric wafer active sensors for structural health monitoring. J Nondestruct Eval 26:123–134

    Article  Google Scholar 

  13. Dai K, Huang Y, Zong G, Sh W, Huang Z (2013) Experimental case studies wireless and wired sensors. In: Proceedings of SPIE 8694, nondestructive characterization for composite materials, aerospace engineering, civil infrastructure, and homeland security 2013

  14. Lieske U, Dietrich A, Schubert L, Frankenstein B (2012) Wireless system of structural health monitoring based on lamb-waves. In: Proceedings of SPIE 8343, industrial and commercial applications of smart structures technologies, 83430B

  15. Doebling SW, Farrar CR, Prime MB (1998) A summary review of vibration-based damage identification methods. Shock Vib Dig 30(2):91–105

    Article  Google Scholar 

  16. Bernal D (2002) Load vectors for damage localization. J Eng Mech 128(1):7–14

    Article  MathSciNet  Google Scholar 

  17. Bernal D (2014) Damage localization and quantification from the image of changes in flexibility. J Eng Mech 140(2):279–286

    Article  Google Scholar 

  18. Todd MD, Nichols JM, Trickey ST, Seaver M, Nichols CJ, Virgin LN (2007) Bragg grating-based fibre optic sensors in structural health monitoring. Phil Trans R Soc A 365:317–343

    Article  ADS  Google Scholar 

  19. Rice JA, Spencer BFJ (2009) Flexible smart sensor framework for autonomous full-scale structural health monitoring. NSEL Report Series, Report No. NSEL-018, Department of Civil and Environmental Engineering, University of Illinois at Urbana-Champaign

  20. Cao DQ, Tucker RW (2008) Nonlinear dynamics of elastic rods using the Cosserat theory: modeling and simulation. Int J Solids Struct 45:460–477

    Article  MATH  Google Scholar 

  21. Loeve MM (1955) Probability Theory, Van Nostrand

  22. Sirovich L (1987) Turbulence and the dynamics of coherent structures, Pt.1. Quart Appl Math 45:561–571

    MATH  MathSciNet  Google Scholar 

  23. Aubry N, Holmes P, Lumley LJ, Stone E (1988) The dynamics of coherent structures in the wall region of a turbulent boundary layer. J Fluid Mech 192:115–173

    Article  ADS  MATH  MathSciNet  Google Scholar 

  24. Cusumano JP, Sharkady MT, Kimble BW (1994) Experimental measurements of dimensionality and spatial coherence in the dynamics of a flexible-beam impact oscillator. Phil Trans R Soc Lond 34:421–438

    Article  ADS  Google Scholar 

  25. Georgiou IT, Schwartz IB (1996) A proper orthogonal decomposition approach to coupled structural-mechanical dynamical systems. ASME-IMECE symposium on nonlinear dynamics and controls DE-vol 91, 17–22 Nov, Atlanta, pp 7–12

  26. Fenny BF, Kappagantu R (1998) On the physical interpretation of proper orthogonal modes in vibrations. J Sound Vib 211(4):607–616

    Article  ADS  Google Scholar 

  27. Georgiou IT, Schwartz IB (1999) Dynamics of large scale coupled structural-mechanical systems: a singular perturbation-proper orthogonal decomposition approach. SIAM J Appl Math 59(4):1178–1207

    Article  MATH  MathSciNet  Google Scholar 

  28. Georgiou IT, Schwartz IB, Emaci M, Vakakis A (1999) Interaction between slow and fast oscillations in an infinite degree-of-freedom linear system coupled to a nonlinear subsystem: theory and experiment. ASME J Appl Mech 66:448–459

    Article  Google Scholar 

  29. Galvanetto U, Violaris G (2007) Numerical investigation of a new damage detection method based on proper orthogonal decomposition. Mech Syst Signal Process 21:1346–1361

    Article  ADS  Google Scholar 

  30. Georgiou IT (2011) Advanced processing of collocated accelerations signals in symmetric beam-like structures with applications to damage detection in a propeller. J Intell Mater Syst Struct 22(12):1371–1394

    Article  MathSciNet  Google Scholar 

  31. Georgiou IT (2008) Characterization of nonlinear coupled dynamics of sandwich structures. In: Proceedings ASME international mechanical engineering congress and exposition, Oct 31–Nov 6, 2008, Boston

  32. Georgiou IT (2005) Advanced proper orthogonal decomposition tools: using reduced models to identify normal modes of vibration and slow invariant manifolds in the dynamics of planar nonlinear rods. Nonlinear Dyn 41:69–110

    Article  MATH  MathSciNet  Google Scholar 

  33. Kersen G, Golinval JC, Vakakis AF, Bergman LA (2005) The method of proper orthogonal decomposition for dynamical characterization and order reduction of mechanical systems: an overview. Nonlinear Dyn 41:147–169

    Article  Google Scholar 

  34. Lanata F, Del Grosso A (2006) Damage detection and localization for continuous static monitoring of structures using a proper orthogonal decomposition of signals. Smart Mater Struct 15:1811–1829

    Article  ADS  Google Scholar 

  35. Vanlanduit S, Parloo E, Cauberghe B, Guillaune P, Verboven P (2005) A robust singular value decomposition for damage detection under changing operating conditions and structural uncertainties. J Sound Vib 284:1033–1050

    Article  ADS  Google Scholar 

  36. Rubin MB (2000) Cosserate theories: shells, rods and points. Kluewer Academic, Dordrecht

    Book  Google Scholar 

  37. Soedel W (2003) Vibrations of shells and plates, 3rd edn. Marcel Dekker, Inc., New York

    Google Scholar 

  38. Newland DE (2005) An introduction to random vibrations, spectral & wavelet analysis, 3rd edn. Dover Publications Inc, New York

    Google Scholar 

  39. Georgiou, IT (2010) Characterizing time and space scales in distributed acceleration signals in aluminum structures. In: Proceedings of the 16th US national congress of theoretical and applied, June 27–July 2, 2010, State College

  40. Reddy JN (2004) An introduction to nonlinear finite element analysis. Oxford University Press, New York

    Book  MATH  Google Scholar 

  41. Georgiou IT, Bajaj AK, Corless M (1998) Slow and fast invariant manifolds, and normal modes in a two- degree-of-freedom structural dynamical system with multiple equilibrium states. Int J Non-Linear Mech 33(2):275–300

    Article  MATH  MathSciNet  Google Scholar 

  42. Ingard KU (1988) Fundamentals of waves and oscillations. Cambridge University Press, New York

    MATH  Google Scholar 

  43. Strogatz SH (1994) Nonlinear dynamics and chaos with applications to physics, biology, chemistry and engineering. Perseus Books Publishing, Reading

    Google Scholar 

  44. Shevtsov S, Zhilyaev I, Akopyan V, Remizov V (2013) A probabilistic approach to the crack identification in the beam-like structure described by Timoshenko beam model. In: 9th international conference on fracture & strength of solids, June 9–1, Jeju

  45. Silva-Muñoz RA, Lopez-Anido RA (2009) Structural health monitoring of marine composite structural joints using embedded fiber Bragg grating strain sensors. Compos Struct 89(2):224–234

    Article  Google Scholar 

  46. Palmieri G, Martarelli M, Palpacelli M, Coronary L (2014) Configuration-dependent modal analysis of a Cartesian parallel kinematics manipulator: numerical modeling and experimental validation. Meccanica 49(4):961–972

    Article  MATH  Google Scholar 

  47. Romano G, Barretta R, Diaco M (2014) Geometric continuum mechanics. Meccanica 49(1):111–133

    Article  MATH  MathSciNet  Google Scholar 

  48. Ubertini F (2013) On damage detection by continuous dynamics monitoring in wind-excited suspension bridges. Meccanica 48(5):1031–1051

    Article  MATH  MathSciNet  Google Scholar 

  49. Bath K-J (1982) Finite element procedures in engineering analysis. Prentice-Hall, Englewood Cliffs

    Google Scholar 

  50. Bowen RM, Wang C-C (1980) Introduction to vectors and tensors: linear and multilinear algebra. Plenum Press, New York

    MATH  Google Scholar 

  51. Rega G, Alaggio R (2001) Spatio-temporal dimensionality in the overall complex dynamics of an experimental cable/mass system. Int J Solids Struct 38:2049–2068

    Article  MATH  Google Scholar 

  52. Goss VGA (2003) Snap buckling, writhing, and loop formation in twisted rods. Dissertation, University of London

  53. Fenny BF (2002) On proper orthogonal coordinates as indicators of modal activity. J Sound Vib 255(5):805–817

    Article  ADS  Google Scholar 

Download references

Author information

Authors and Affiliations

  1. Dynamics-Acoustics & Diagnostics of Complex Systems Laboratory, School of Naval Architecture & Marine Engineering, National Technical University of Athens, Athens, Greece

    Ioannis T. Georgiou

  2. School of Mechanical Engineering, Purdue University, West Lafayette, IN, USA

    Ioannis T. Georgiou

Authors
  1. Ioannis T. Georgiou
    View author publications

    You can also search for this author in PubMed Google Scholar

Corresponding author

Correspondence to Ioannis T. Georgiou.

Rights and permissions

Reprints and permissions

About this article

Check for updates. Verify currency and authenticity via CrossMark

Cite this article

Georgiou, I.T. A single pair-of-sensors technique for geometry consistent sensing of acceleration vector fields in beam structures: damage detection and dissipation estimation by POD modes. Meccanica 50, 1303–1330 (2015). https://doi.org/10.1007/s11012-014-0091-y

Download citation

  • Received:

  • Accepted:

  • Published:

  • Issue Date:

  • DOI: https://doi.org/10.1007/s11012-014-0091-y

Keywords

Search

Navigation