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Characterization of Nonlinear Dynamics for a Highway Bridge in Alaska

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Abstract

Purpose and Methods

This research studies the nonlinear dynamic feature of the Chulitna river bridge in Alaska USA. The acceleration response of the bridge under moving truck loads are evaluated for dynamic invariants. The Fourier spectrum of a free-decay response (after the vehicle passes) exhibits a salient line spectrum, which is correlated to calculated linear modes from a 3-D finite element analysis. The bridge deck is used shell elements and truss members are simulated with beam elements.

Results

At some locations on bridge, the Fourier spectrum of the bridge response to vehicle loading exhibits a complicated narrow bandwidth suggesting the possibility of nonlinear characteristics. Chaos dynamics invariants of the response are examined based on the largest Lyapunov exponents, correlation dimension, and K-entropy and used to identify the nonlinear dynamic features.

Conclusions

The bridge was found to have following characteristics: (a) modal parameters extracted from free-decay response exhibit linear properties. The free vibrations have relatively small amplitude which is not sensitive to possible structure damages; (b) at some locations, measured responses to moving loads exhibit chaos nonlinear dynamics properties with specific signatures. All of the derived nonlinear dynamics invariants including Lyapunov exponents, correlation dimension, and K-entropy support this observation; and (c) in addition to linear modal parameters, the multiple nonlinear dynamics invariants with damage-sensitive features can be used as additional candidates for the ongoing bridge health monitoring.

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References

  1. Oh BH, Jung BS (1998) Structural damage assessment with data of static and modal tests. J Struct Eng 124(8):956–965

    Article  Google Scholar 

  2. Sohn H, Farrar CR, Hemez FM, Shunk DD, Stinemates DW, Nadler BR (2003) A review of structural health monitoring literature: 1996–2001. Report LA-13976-MS. Los Alamos National Laboratory, Los Alamos

    Google Scholar 

  3. Salawu OS (1997) Detection of structural damage through changes in frequency: a review. J Eng Struct 19(9):718–723

    Article  Google Scholar 

  4. Pandey AK, Biswas M (1994) Damage detection in structures using changes in flexibility. J Sound Vib 169(1):3–17

    Article  Google Scholar 

  5. Whalen TM (2008) The behaviour of higher order mode shape derivatives in damaged beam-like structures. J Sound Vib 309(3–5):426–464

    Article  Google Scholar 

  6. Zatar W, Harik I, Ren WX, Zhao T (2008) Seismic risk assessment of priority bridges along I-24 in Western Kentucky. In: The sixth national seismic conference on bridges & highways, July 27–30, 2008, Charleston, South Carolina

  7. Ren WX, Zatar W, Harik I (2004) Ambient vibration-based seismic evaluation of a continuous girder bridge. Eng Struct 26(5):631–640

    Article  Google Scholar 

  8. Li J, Law S, Hao H (2013) Improved damage identification in bridge structures subject to moving loads: numerical and experimental studies. Int J Mech Sci 74(2013):99–111

    Article  Google Scholar 

  9. Huffman JT, Xiao F, Chen G, Hulsey JL (2015) Detection of soil-abutment interaction by monitoring bridge response using vehicle excitation. J Civ Struct Health Monit 5(4):389–395

    Article  Google Scholar 

  10. Xiao F, Hulsey JL, Cheng GS (2015) Multi-direction bridge model updating using static and dynamic measurement. Appl Phys Res 7(1):47

    Article  Google Scholar 

  11. Klepka A, Straczkiewicz M, Piezonka L, Stazewski WJ, Gelman L, Aymerich F, Uhl T (2015) Triple correlation for detection of damage-related nonlinearities in composite structures. Nonlinear Dyn 81(1):483–486

    MathSciNet  Google Scholar 

  12. Lo KF, Ni SH, Huang YH (2010) Non-destructive test for pile beneath bridge in the time, frequency, and time-frequency domains using transient loading. Nonlinear Dyn 62(1):349–360

    Article  Google Scholar 

  13. Jin S, Livingston RA, Marzougui D (2001) Lyapunov exponent maps applied to damage detection of aging nonlinear highway infrastructures. In: Proceeding of SPIE 4337, health monitoring and management of civil infrastructure systems, p 411

  14. Livingston RA, Jin S, Marzougui D (2001) Application of nonlinear dynamics analysis to damage detection and health monitoring of highway structures. In: Proceeding of SPIE—the international society for optical engineering, vol 4337. Society of Photo-Optical Instrumentation Engineers, Newport Beach, pp 402–410

  15. Casciati Fabio, Casciati Sara (2006) Structural health monitoring by Lyapunov exponents of non-linear time series. Struct Control Health Monit 13:132–146

    Article  Google Scholar 

  16. Moniz L, Nichols JM, Nichols CJ, Seaver M, Trickey ST, Todd MD, Pecora LM, Virgin LN (2005) A multivariate, attractor-based approach to structural health monitoring. J Sound Vib 283:295–310

    Article  Google Scholar 

  17. Worden K, Farrar CR et al (2007) The fundamental axioms of structural health monitoring. Proc R Soc Lond Ser A (Mathematical, Physical and Engineering Sciences) 463(2082):1639–1664

    Article  Google Scholar 

  18. Kantz H, Schreiber T (1997) Nonlinear time series analysis [M]. Cambridge University Press, Cambridge

    MATH  Google Scholar 

  19. Brown R, Bryant P, Abarbanel HDI (1991) Computing the Lyapunov exponents of a dynamical system from observed time series. Phys Rev A 34:2787–2806

    Article  Google Scholar 

  20. Rossenstein MT, Collins JJ, Deluca CJ (1993) A practical method for calculating largest Lyapunov exponents from small data sets. Phys D 65(1):117–134

    Article  MathSciNet  Google Scholar 

  21. Takens F (1981) Determining strange attractors in turbulence. Lect Notes Math 898:361–381

    MATH  Google Scholar 

  22. Cao L (1997) Practical method for determining the minimum embedding dimension of a scalar time series. Phys D 110(1):43–50

    Article  Google Scholar 

  23. Grassberger P (1983) Procaccia I, Characterization of strange attractors. Phys Rev Lett A 50(5):346–349

    Article  Google Scholar 

  24. Grassberger P, Procaccia I (1983) Estimation of the Kolmogorov entropy from a chaotic signal. Phys Rev A 28(4):2591–2593

    Article  Google Scholar 

  25. Schouten JC (1994) Maximum-likelihood estimation of the entropy of an attractor. Phys Rev E 49(1):126–129

    Article  MathSciNet  Google Scholar 

  26. Xiao F, Chen GS, Hulsey JL, Dolan JD, Dong Y (2016) Ambient loading and modal parameters for the Chulitna river bridge. Adv Struct Eng 19(4):660–670

    Article  Google Scholar 

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Acknowledgements

The authors acknowledge the support of Professor Helen Liu in University of Alaska Anchorage, Alaska Department of Transportation & Public Facilities. The author wishes to dedicate this paper to the memory of his classmate in college, Dr. Shuang Jin, former Senior Scientist in the Federal Highway Administration USA, one of the earliest pioneers applying chaos theory to bridge health monitoring.

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Authors and Affiliations

  1. Department of Civil Engineering, Nanjing University of Science and Technology, Nanjing, China

    Feng Xiao

  2. College of IT and Engineering, Marshall University, Huntington, WV, USA

    Gang S. Chen & Wael Zatar

  3. Department of Civil and Environmental Engineering, University of Alaska Fairbanks, Fairbanks, AK, USA

    J. Leroy Hulsey

Authors
  1. Feng Xiao
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  2. Gang S. Chen
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  3. J. Leroy Hulsey
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  4. Wael Zatar
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Corresponding author

Correspondence to Gang S. Chen.

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Xiao, F., Chen, G.S., Hulsey, J.L. et al. Characterization of Nonlinear Dynamics for a Highway Bridge in Alaska. J. Vib. Eng. Technol. 6, 379–386 (2018). https://doi.org/10.1007/s42417-018-0048-x

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  • DOI: https://doi.org/10.1007/s42417-018-0048-x

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