Detecting the position of non-linear component in periodic structures from the system responses to dual sinusoidal excitations

International Journal of Non-Linear Mechanics

Volumn 42, Issue 9, 2007, Pages 1074-1083

  Peng, Z K ^a   Lang, Z Q ^a  

^a UNIVERSITY OF SHEFFIELD   (United Kingdom)

Author keywords

Fault detection; Non linear output frequency response function; Non linear vibration; Periodic structure; Volterra series

Indexed keywords

DIAGNOSIS; FREQUENCY RESPONSE; NONLINEAR ANALYSIS; NONLINEAR SYSTEMS; NUMERICAL METHODS; VIBRATION ANALYSIS;

NONLINEAR OUTPUT FREQUENCY RESPONSE FUNCTION; SINUSOIDAL EXCITATIONS; VOLTERRA SERIES;

PERIODIC STRUCTURES;

EID: 35649002587     PISSN: 00207462     EISSN: None     Source Type: Journal    
DOI: 10.1016/j.ijnonlinmec.2007.06.002     Document Type: Article

References (25)

1. Duhame D., Maceb B.R., and Brennan M.J. Finite element analysis of the vibrations of waveguides and periodic structures. J. Sound Vib. 294 (2006) 205-220
2. Luongo A., and Romeo F. Real wave vectors for dynamic analysis of periodic structures. J. Sound Vib. 279 (2005) 309-325
3. Romeo F., and Luongo A. Vibration reduction in piecewise bi-coupled periodic structures. J. Sound Vib. 268 (2003) 601-615
4. Wei J., and Petyt M. A method of analyzing finite periodic structures, part 1: theory and examples. J. Sound Vib. 202 (1997) 555-569
5. Mukherjee S., and Parthan S. Normal modes and acoustic response of finite one- and two-dimensional multi-bay periodic panels. J. Sound Vib. 197 (1996) 527-545
6. Yuan J., and Dickinson S.M. On the determination of phase constants for the study of the free vibration of periodic structures. J. Sound Vib. 179 (1995) 369-383
7. Fassois S.D., and Sakellariou J.S. Stochastic output error vibration-based damage detection and assessment in structures under earthquake excitation. J. Sound Vib. 297 (2006) 1048-1067
8. Mead D.J. Wave propagation in continuous periodic structures: research contributions from Southampton, 1964-1995. J. Sound Vib. 190 (1996) 495-524
9. Chi C.-C., and Rosenberg R.M. On damped non-linear dynamic systems with many degrees of freedom. Int. J. Non-Linear Mech. 20 (1985) 371-384
10. Vakakis A.F., King M.E., and Pearlstein A.J. Forced localization in a periodic chain of non-linear oscillators. Int. J. Non-Linear Mech. 29 (1994) 429-447
11. Royston T.J., and Singh R. Periodic response of mechanical systems with local non-linearities using an enhanced Galerkin technique. J. Sound Vib. 194 (1996) 243-263
12. Chakraborty G., and Mallik A.K. Dynamics of a weakly non-linear periodic chain. Int. J. Non-Linear Mech. 36 (2001) 375-389
13. Marathe A., and Chatterjee A. Wave attenuation in nonlinear periodic structures using harmonic balance and multiple scales. J. Sound Vib. 289 (2006) 871-888
14. Neild S.A., Mcfadden P.D., and Williams M.S. A discrete model of vibrating beam using time-stepping approach. J. Sound Vib. 239 (2001) 99-121
15. Zhu H., and Wu M. The characteristic receptance method for damage detection in large mono-coupled periodic structures. J. Sound Vib. 251 (2002) 241-259
16. Fassois S.D., and Sakellariou J.S. Time-series methods for fault detection and identification in vibrating structures. Philos. Trans. R. Soc. London Ser. A Math. Phys. Eng. Sci. 365 (2007) 411-448
17. Worden K., Manson G., and Tomlinson G.R. A harmonic probing algorithm for the multi-input Volterra series. J. Sound Vib. 201 (1997) 67-84
18. Lang Z.Q., and Billings S.A. Output frequency characteristics of nonlinear system. Int. J. Control 64 (1996) 1049-1067
19. Billings S.A., and Tsang K.M. Spectral analysis for nonlinear system, part I: parametric non-linear spectral analysis. Mech. Syst. Signal Process. 3 (1989) 319-339
20. Billings S.A., and Peyton Jones J.C. Mapping nonlinear integro-differential equations into the frequency domain. Int. J. Control 52 (1990) 863-879
21. Peyton Jones J.C., and Billings S.A. A recursive algorithm for the computing the frequency response of a class of nonlinear difference equation models. Int. J. Control 50 (1989) 1925-1940
22. Lang Z.Q., and Billings S.A. Energy transfer properties of nonlinear systems in the frequency domain. Int. J. Control 78 (2005) 354-362
23. Z.K. Peng, Z.Q. Lang, S.A. Billings, Nonlinear output frequency response functions of MDOF systems with multiple nonlinear components, Int. J. Non-Linear Mech. (2007), Doi:10.1016/j.ijnonlinmec.2007.04.001.
24. Lang Z.Q., and Billings S.A. Output frequencies of nonlinear systems. Int. J. Control 67 (1997) 713-730
25. Peng Z.K., Lang Z.Q., and Billings S.A. Resonances and resonant frequencies for a class of nonlinear systems. J. Sound Vib. 300 (2007) 993-1014