Skip to main content
SpringerLink
Log in

Effects of damage parametric changes on the aeroelastic behaviors of a damaged panel

  • Original paper
  • Published:
Nonlinear Dynamics Aims and scope Submit manuscript

Abstract

In this study, the aeroelastic responses and stability boundaries of a simply supported supersonic plate with structural damage are investigated to assess the effects of damage parametric changes on the stability regions as well as to explore some potential tools for damage detection. In the modeling, structural damage is a local bending stiffness loss with various levels, extents and positions. The effects of damage level, extent and position are presented via exploiting nonlinear tools such as bifurcation diagrams, stability regions, Poincaré maps and Lyapunov exponents. Specially, the proper orthogonal decomposition (POD) method is applied to extract the POD modes to detect the damage parametric variations. It is determined that (1) structural damage has a notable influence on the aeroelastic stability of the panel; (2) the damage level and extent affect in a similar way that a larger damage level/extent tends to reduce the flutter boundary for a flat plate, but conversely increase the flutter boundary for a buckled plate; (3) the damage occurring around the leading of the panel corresponds to the least stable panel compared to the other positions along the chordwise; (4) the stability region as a novel way for damage detection is proved to be sensitive and effective, and the largest Lyapunov exponent as a quantitative measure is powerful to reveal the subtle differences in the chaos induced by damage changes; (5) the higher-order POD modes are more sensitive to the subtle damage than the primary POD modes.

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
Fig. 17
Fig. 18
Fig. 19
Fig. 20
Fig. 21
Fig. 22
Fig. 23
Fig. 24
Fig. 25
Fig. 26
Fig. 27

Similar content being viewed by others

Abbreviations

a :

Plate length (m)

D :

Plate stiffness (Nm)

E :

Young’s modulus (\(\hbox {N}/\hbox {m}^2\))

h :

Plate thickness (m)

M :

Number of modes retained

\(M_a\) :

Mach number

m, n :

Mode number

\(N_{x}^T\) :

In-plane thermal force in x direction (N/m)

\(p-p_{\infty }\) :

Aerodynamic pressure (\(\hbox {N}/\hbox {m}^2\))

q :

\(\rho U^2/2\), dynamic pressure (\(\hbox {N}/\hbox {m}^2\))

T :

Temperature differential (K)

t :

Time (s)

U :

Velocity (m/s)

w :

Panel transverse deflection (m)

x :

Streamwise coordinate (m)

\(\alpha \) :

Thermal expansion coefficient (\(/^\circ \hbox {C}\))

\(\beta \) :

\((M_a^2-1)^{1/2}\)

\(\nu \) :

Poisson ratio

\(\psi \) :

POD mode

\(\rho \), \(\rho _m\) :

Air density, plate density (\(\hbox {kg}/\hbox {m}^3\))

References

  1. Abdelkefi, A., Vasconcellos, R., Nayfeh, A.H., Hajj, M.R.: Online damage detection via a synergy of proper orthogonal decomposition and recursive Bayesian filters. Nonlinear Dyn. 71(1–2), 159–173 (2013)

    Article  MATH  Google Scholar 

  2. Alder, M.: Development and validation of a partitioned fluid-structure solver for transonic panel flutter with focus on boundary layer effects. In: 44th AIAA Fluid Dynamics Conference, p. 2448 (2014)

  3. Azam, S.E., Mariani, S., Attari, N.K.A.: Online damage detection via a synergy of proper orthogonal decomposition and recursive Bayesian filters. Nonlinear Dyn. 89(2), 1489–1511 (2017)

    Article  Google Scholar 

  4. Boyer, N.R., McNamara, J.J., Gaitonde, D.V., Barnes, C.J., Visbal, M.R.: Study on shock-induced panel flutter in 3-d inviscid flow. In: 58th AIAA/ASCE/AHS/ASC Structures, Structural Dynamics, and Materials Conference, p. 0404 (2017)

  5. Chen, G., Sun, J., Li, Y.M.: Active flutter suppression control law design method based on balanced proper orthogonal decomposition reduced order model. Nonlinear Dyn. 70(1), 1–12 (2012)

    Article  MathSciNet  Google Scholar 

  6. Chen, G., Zhou, Q., Da Ronch, A., Li, Y.: Computational fluid dynamics-based aero-servo-elastic analysis for gust load alleviation. J. Aircr. 55, 1619–1628 (2017)

    Article  Google Scholar 

  7. Cheng, G., Mei, C.: Finite element modal formulation for hypersonic panel flutter analysis with thermal effects. AIAA J. 42(4), 687–695 (2004)

    Article  Google Scholar 

  8. Dai, H., Jing, X., Wang, Y., Yue, X., Yuan, J.: Post-capture vibration suppression of spacecraft via a bio-inspired isolation system. Mech. Syst. Signal Process. 105, 214–240 (2018)

    Article  Google Scholar 

  9. Doebling, S.W., Farrar, C.R., Prime, M.B., et al.: A summary review of vibration-based damage identification methods. Shock Vib. Dig. 30(2), 91–105 (1998)

    Article  Google Scholar 

  10. Dowell, E.H.: Nonlinear oscillations of a fluttering plate. AIAA J. 4(7), 1267–1275 (1966)

    Article  Google Scholar 

  11. Dugundji, J., Dowell, E.H., Perkin, B.: Subsonic flutter of panels on a continuous elastic foundation. AIAA J. 1(5), 1146–1154 (1963)

    Article  Google Scholar 

  12. Eftekhari, S., Bakhtiari-Nejad, F., Dowell, E.: Bifurcation boundary analysis as a nonlinear damage detection feature: does it work? J. Fluids Struct. 27(2), 297–310 (2011)

    Article  Google Scholar 

  13. Eftekhari, S., Bakhtiari-Nejad, F., Dowell, E.: Damage detection of an aeroelastic panel using limit cycle oscillation analysis. Int. J. Non Linear Mech. 58, 99–110 (2014)

    Article  Google Scholar 

  14. Epureanu, B.I., Tang, L.S., Paidoussis, M.P.: Exploiting chaotic dynamics for detecting parametric variations in aeroelastic systems. AIAA J. 42(4), 728–735 (2004)

    Article  Google Scholar 

  15. Epureanu, B.I., Yin, S.H., Dowell, E.H.: Enhanced nonlinear dynamics for accurate identification of stiffness loss in a thermo-shielding panel. Nonlinear Dyn. 39, 197–211 (2005)

    Article  MATH  Google Scholar 

  16. Fan, W., Qiao, P.: Vibration-based damage identification methods: a review and comparative study. Struct. Health Monit. 10(1), 83–111 (2011)

    Article  Google Scholar 

  17. Galvanetto, U., Surace, C., Tassotti, A.: Structural damage detection based on proper orthogonal decomposition: experimental verification. AIAA J. 46(7), 1624 (2008)

    Article  Google Scholar 

  18. Galvanetto, U., Violaris, G.: Numerical investigation of a new damage detection method based on proper orthogonal decomposition. Mech. Syst. Signal Process. 21(3), 1346–1361 (2007)

    Article  Google Scholar 

  19. Ganji, H.F., Dowell, E.H.: Panel flutter prediction in two dimensional flow with enhanced piston theory. J. Fluids Struct. 63, 97–102 (2016)

    Article  Google Scholar 

  20. Gray, C.E., Mei, C.: Large-amplitude finite element flutter analysis of composite panels in hypersonic flow. AIAA J. 31(6), 1090–1099 (1993)

    Article  MATH  Google Scholar 

  21. Guo, X., Mei, C.: Application of aeroelastic modes on nonlinear supersonic panel flutter at elevated temperatures. Comput. Struct. 84(24), 1619–1628 (2006)

    Article  Google Scholar 

  22. Li, H., Huang, Y., Ou, J., Bao, Y.: Fractal dimension-based damage detection method for beams with a uniform cross-section. Comput. Aided Civ. Infrastruct. Eng. 26(3), 190–206 (2011)

    Article  Google Scholar 

  23. Lock, M.H., Fung, Y.C.: Comparative experimental and theoretical studies of the flutter of flat panels in a low supersonic flow. In: Air Force Office of Scientific Research TN, vol. 670 (1961)

  24. Manoach, E., Samborski, S., Mitura, A., Warminski, J.: Vibration based damage detection in composite beams under temperature variations using poincare maps. Int. J. Mech. Sci. 62(1), 120–132 (2012)

    Article  Google Scholar 

  25. Mei, C.: A finite-element approach for nonlinear panel flutter. AIAA J. 15, 1107–1110 (1977)

    Article  Google Scholar 

  26. Moniz, L., Nichols, J., Nichols, C., Seaver, M., Trickey, S., Todd, M., Pecora, L., Virgin, L.: A multivariate, attractor-based approach to structural health monitoring. J. Sound Vib. 283(1), 295–310 (2005)

    Article  Google Scholar 

  27. Moon, F.C.: Chaotic Vibrations: An Introduction for Applied Scientists and Engineers. Wiley, New York (1987)

    MATH  Google Scholar 

  28. Mortara, S., Slater, J., Beran, P.: Analysis of nonlinear aeroelastic panel response using proper orthogonal decomposition. ASME J. Vib. Acoust. 126(3), 416–421 (2004)

    Article  Google Scholar 

  29. Nichols, J., Todd, M., Seaver, M., Virgin, L.: Use of chaotic excitation and attractor property analysis in structural health monitoring. Phys. Rev. E 67(1), 016,209 (2003a)

    Article  Google Scholar 

  30. Nichols, J., Virgin, L., Todd, M., Nichols, J.: On the use of attractor dimension as a feature in structural health monitoring. Mech. Syst. Signal Process. 17(6), 1305–1320 (2003b)

    Article  Google Scholar 

  31. Rucka, M., Wilde, K.: Application of continuous wavelet transform in vibration based damage detection method for beams and plates. J. Sound Vib. 297(3), 536–550 (2006)

    Article  Google Scholar 

  32. Shane, C., Jha, R.: Proper orthogonal decomposition based algorithm for detecting damage location and severity in composite beams. Mech. Syst. Signal Process. 25(3), 1062–1072 (2011)

    Article  Google Scholar 

  33. Song, Z., Li, F.: Aerothermoelastic analysis of nonlinear composite laminated panel with aerodynamic heating in hypersonic flow. Compos. Part B Eng. 56, 830–839 (2014)

    Article  Google Scholar 

  34. Song, Z.G., Zhang, L.W., Liew, K.M.: Aeroelastic analysis of cnt reinforced functionally graded composite panels in supersonic airflow using a higher-order shear deformation theory. Compos. Struct. 141, 79–90 (2016)

    Article  Google Scholar 

  35. Sprott, J.C.: Chaos and Time-Series Analysis, pp. 116–117. Oxford University Press, Oxford (2003)

    MATH  Google Scholar 

  36. Strganac, T.W., Kim, Y.I.: Aeroelastic behavior of composite plates subject to damage growth. J. Aircr. 33(1), 68–73 (1996)

    Article  Google Scholar 

  37. Tian, W., Yang, Z., Gu, Y., Wang, X.: Analysis of nonlinear aeroelastic characteristics of a trapezoidal wing in hypersonic flow. Nonlinear Dyn. 89(2), 1205–1232 (2017)

    Article  Google Scholar 

  38. Trendafilova, I., Manoach, E.: Vibration-based damage detection in plates by using time series analysis. Mech. Syst. Signal Process. 22(5), 1092–1106 (2008)

    Article  Google Scholar 

  39. Wang, X., Yang, Z., Wang, W., Tian, W.: Nonlinear viscoelastic heated panel flutter with aerodynamic loading exerted on both surfaces. J. Sound Vib. 409, 306–317 (2017a)

    Article  Google Scholar 

  40. Wang, Y., Li, F., Wang, Y., Jing, X.: Nonlinear responses and stability analysis of viscoelastic nanoplate resting on elastic matrix under 3: 1 internal resonances. Int. J. Mech. Sci. 128, 94–104 (2017b)

    Article  Google Scholar 

  41. Wolf, A., Swift, J.B., Swinney, H.L., Vastano, J.A.: Determining lyapunov exponents from a time series. Physica D Nonlinear Phenom. 16, 285–317 (1985)

    Article  MathSciNet  MATH  Google Scholar 

  42. Xie, D., Xu, M.: A comparison of numerical and semi-analytical proper orthogonal decomposition methods for a fluttering plate. Nonlinear Dyn. 79(3), 1971–1989 (2015)

    Article  MATH  Google Scholar 

  43. Xie, D., Xu, M., Dai, H., Dowell, E.H.: Observation and evolution of chaos for a cantilever plate in supersonic flow. J. Fluids Struct. 50, 271–291 (2014a)

    Article  Google Scholar 

  44. Xie, D., Xu, M., Dai, H., Dowell, E.H.: Proper orthogonal decomposition method for analysis of nonlinear panel flutter with thermal effects in supersonic flow. J. Sound Vib. 337, 263–283 (2015)

    Article  Google Scholar 

  45. Xie, D., Xu, M., Dowell, E.H.: Proper orthogonal decomposition reduced-order model for nonlinear aeroelastic oscillations. AIAA J. 52(2), 1–13 (2014b)

    Article  Google Scholar 

  46. Yam, L., Yan, Y., Jiang, J.: Vibration-based damage detection for composite structures using wavelet transform and neural network identification. Compos. Struct. 60(4), 403–412 (2003)

    Article  Google Scholar 

  47. Ye, W.L., Dowell, E.H.: Limit cycle oscillation of a fluttering cantilever plate. AIAA J. 29(11), 1929–1936 (1991)

    Article  MATH  Google Scholar 

Download references

Acknowledgements

The authors would like to acknowledge the support of Grant 3102016ZY004 from Northwestern Polytechnical University, China, and the fund of Grant 11502203 from Chinese NSF.

Author information

Authors and Affiliations

  1. College of Astronautics, Northwestern Polytechnical University, Xi’an, 710072, China

    Dan Xie, Min Xu & Honghua Dai

Authors
  1. Dan Xie
    View author publications

    You can also search for this author in PubMed Google Scholar

  2. Min Xu
    View author publications

    You can also search for this author in PubMed Google Scholar

  3. Honghua Dai
    View author publications

    You can also search for this author in PubMed Google Scholar

Corresponding author

Correspondence to Dan Xie.

Ethics declarations

Conflict of interest

The authors declare that they have no conflict 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

Xie, D., Xu, M. & Dai, H. Effects of damage parametric changes on the aeroelastic behaviors of a damaged panel. Nonlinear Dyn 97, 1035–1050 (2019). https://doi.org/10.1007/s11071-019-05029-y

Download citation

  • Received:

  • Accepted:

  • Published:

  • Issue Date:

  • DOI: https://doi.org/10.1007/s11071-019-05029-y

Keywords

Search

Navigation