SpringerLink
Log in

Signal Analysis in Multibody Systems

  • Chapter
Advanced Multibody System Dynamics

Part of the book series: Solid Mechanics and Its Applications ((SMIA,volume 20))

  • 503 Accesses

Abstract

During the last decades there has been rapid progress in understanding the dynamics of deterministic nonlinear systems, especially chaotic ones. The deterministic unpredictable behaviour of nonlinear dynamical systems has become a very interesting subject in many fields of science. Therefore, it is strongly desirable to develop powerful methods which are applicable in the analysis of mechanical multibody systems, to extract physical quantities from simulation or from experimentally obtained signals.

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

Access this chapter

Log in via an institution

Subscribe and save

Springer+ Basic
EUR 32.99 /Month
  • Get 10 units per month
  • Download Article/Chapter or Ebook
  • 1 Unit = 1 Article or 1 Chapter
  • Cancel anytime
Subscribe now

Buy Now

Chapter
USD 29.95
Price excludes VAT (USA)
  • Available as PDF
  • Read on any device
  • Instant download
  • Own it forever
eBook
USD 169.00
Price excludes VAT (USA)
  • Available as PDF
  • Read on any device
  • Instant download
  • Own it forever
Softcover Book
USD 219.99
Price excludes VAT (USA)
  • Compact, lightweight edition
  • Dispatched in 3 to 5 business days
  • Free ship** worldwide - see info
Hardcover Book
USD 219.99
Price excludes VAT (USA)
  • Durable hardcover edition
  • Dispatched in 3 to 5 business days
  • Free ship** worldwide - see info

Tax calculation will be finalised at checkout

Purchases are for personal use only

Institutional subscriptions

Preview

Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.

Similar content being viewed by others

References

  1. Aleksic, Z.: Estimating the Embedding Dimension. Physica D52, 1991, 362–368.

    MathSciNet  MATH  Google Scholar 

  2. Bajkowski, J.; Müller, P.C.: Lyapunov Exponents and Fractal Dimensions in Nonlinear Mechanical Systems. ZAMM, 68, 1988, 49–53.

    Google Scholar 

  3. Bajkowski, J.; Müller, P. C.: Programm-Modul MBTFFT. DFG-Report, Mu 448–12, MKS-Signalanalyse, University of Wuppertal, Germany, December 1990.

    Google Scholar 

  4. Bajkowski, J.; Müller, P. C.: Programm-Modul MBYLAP. DFG Report, Mu 448–12 MKS-Signalanalyse, University of Wuppertal, Germany, August 1992.

    Google Scholar 

  5. Bendat, Y.S.; Piersol, A.G.: Engineering Applications of Correlation and Spectral Analysis. John Wiley Sr Sons 1980.

    Google Scholar 

  6. Benettin, G.; Galgani, L.; Giorgili, A.; Strelcyn, J.M.: Ljapunov Characteristic Exponents for Smooth Dynamical Systems and for Hamiltonian Systems; A Method for Computing all of Them. Part I: Theory. Part II: Numerical Application. Meccanica 15, 1980, 9–30.

    Article  ADS  MATH  Google Scholar 

  7. Bergland, G.D.: A Fast Fourier Transform Algorithm Using Base 8 Iterations. Math. Comp., Vol. 22, 1968, 275–279.

    MathSciNet  MATH  Google Scholar 

  8. Bergland, G.D.: A Radix-Eight Fast Fourier Transform Subroutine for Real-Valued Series. IEEE Trans. on Audio and Electroacoustic., Vol. AU-17(1969), 138–144.

    Google Scholar 

  9. Bestle, G.: Beurteilungskriterien für chaotische Bewegungen nichtlinearer Schwingungssysteme. Fortschritt-Berichte VDI, Reihe 11: Schwingungstechnik Nr. 100. Düsseldorf: VDI-Verlag 1988.

    Google Scholar 

  10. Blackman, R.B.; Tukey, J.W.: The Measurement of Power Spectra. Dover 1958.

    Google Scholar 

  11. Brigham, E.O.: The Fast Fourier Transform and its Applications. Prentice-Hall International Editions 1988.

    Google Scholar 

  12. Broomhead, D.S.; King, G.K.: Extracting Qualitative Dynamics from Experimental Data. Physica D20, 1986, 217–236.

    MathSciNet  MATH  Google Scholar 

  13. Burrus, C.S.; Parks, T.W.: DFT/FFT and Convolution Algorithms. John Wiley Sons 1985.

    Google Scholar 

  14. Buzug, Th.; Pfister, G.: Comparison of Algorithms Calculating Opimal Embedding Parameters for Delay Time Coordinates. Physica D58, 1992, 127–137.

    Google Scholar 

  15. Carter, G. C., Knapp, C. H., Nuttall, A. H.: Estimation of the Magnitude-Squared Coherence Function via Overlapped Fast Fourier Transform Processing. IEEE Trans. Audio Electroaccoustic., AU-21(1973), 337–344.

    Google Scholar 

  16. Cenys, G.; Lasiene, G.; Pyragas, K.: Estimation of Interrelation Between Chaotic Observables. Physica D52, 1991, 332–337.

    MathSciNet  MATH  Google Scholar 

  17. Cooley, J.W.; Tukey, J.W.: An Algorithm for Machine Calculation of Complex Fourier Series. Math. Comp. Vol. 19, 1965, 297–301.

    Article  MathSciNet  MATH  Google Scholar 

  18. Eberhard, A.: An Optimal Discrete Window for the Calculation of Power Spectra. IEEE Trans. Audio and Electroacoustics, AU-21(1973), 37–43.

    Google Scholar 

  19. Eckmann, J.-P.; Ruelle, D.: Ergodic Theory of Chaos and Strange Attractors. Reviews of Modern Physics, Vol. 57, 1985, 617–655.

    Article  MathSciNet  ADS  Google Scholar 

  20. Eckmann, J. P.; Ruelle, D.: Fundamental Limitations for Estimating Dimensions and Lyapunov Exponents in Dynamical Systems. Physica D56, 1992, 185201.

    Google Scholar 

  21. Eckmann, J.-P.; Oliffson, S.; Ruelle, D.; Ciliberto, S.: Liapunov Exponents From Time Series. Physical Review A, Vol. 34, 1086, 4971–4979.

    Article  Google Scholar 

  22. Fraedrich, K.; Wang, R.: A Modified Version of the Grassberger-Procaccia Algorithm via Re-Embedding. In Nonlinear Dynamics: Attractor Approximation and Global Behaviour, Int. Seminar on Applied Math., Sept. 28-Oct. 2, Gaussig, Germany, 1992, 53–81.

    Google Scholar 

  23. Fraser, A.M.: Reconstructiong Attractors from Scalar Time Series: A Comparison of Singular Systems and Redundancy Criteria. Physica D34, 1989, 391–404.

    MathSciNet  MATH  Google Scholar 

  24. Fraser, A.M.; Swinney, H.L.: Independent Coordinates for Strange Attractors From Mutual Information. Physical Reviews A, Vol. 33, 1986, 1134–1140.

    Article  MathSciNet  ADS  MATH  Google Scholar 

  25. Fritzen, C. P.: Reguläres und chaotisches Verhalten einer Laval-Welle mit Riß. ZAMM 70, 1990, 112–114.

    MathSciNet  Google Scholar 

  26. Froehling, H.; Crutchfield, J.P.; Farmer, D.; Packard, N.H.; Shaw, R.: On Determining the Dimension of Chaotic Flows. Physica D3, 1981, 605–617.

    MathSciNet  MATH  Google Scholar 

  27. Gencay, R.; Deckert, W. D.: An Algorithm for the n Lyapunov Exponents of n-Dimensional Unknown Dynamical System. Physica D59, 1992, 142–157.

    MathSciNet  MATH  Google Scholar 

  28. Grassberger, P.; Schreiber, T.; Schaffrath, C.: Non-Linear Time Sequence Analysis Report of Department of Physics, University of Wuppertal, Germany, 1991, 1–46.

    Google Scholar 

  29. Greene, J.M.; Kim, J.-S.: The Calculation of Lyapunov Spectra. Physica D24, 1987, 213–225.

    MathSciNet  MATH  Google Scholar 

  30. Guckenheimer, A.J.; Holmes, P.: Nonlinear Oscillations, Dynamical Systems and Bifurcations of Vector Fields. Springer, New York, 1983.

    MATH  Google Scholar 

  31. Haken, H.: At Least one Lyapunov Exponent Vanishes if the Trajectory of an Attractor Does not Contain a Fixed Point. Phys. Letters A, Vol. 94, 1983, 71–72.

    Article  MathSciNet  ADS  Google Scholar 

  32. Harris, F.J.: On the Use of Windows for Harmonic Analysis with the Discrete Fourier Transform. Proc. IEEE Vol. 66, 1978, 51–83.

    Article  ADS  Google Scholar 

  33. IEEE Digital Signal Processing Committee (ed.): Programs for Digital Signal Processing. IEEE Proc. 1979.

    Google Scholar 

  34. Jansen, J. D.: Nonlinear Rotor Dynamics Applied to Oilwell Drillstring Vibrations. Sound Vibr. 147, 1991, 115–135.

    Article  ADS  Google Scholar 

  35. Kammeyer, K.J.; Kraschel, K.: Digitale Signalverarbeitung. Filterung and Spektralanalyse. B.G. Teubner 1988.

    Google Scholar 

  36. Kim, M.C.; Hsu, C.S.: Computation of the Largest Lyapunov Exponent by the Generalized Cell Map**. J. Statistical Physics, Vol. 45, 1986, 49–61.

    Article  MathSciNet  ADS  MATH  Google Scholar 

  37. Knapp, C.H.; Carter, G.C.: The Generalized Correlation Method for Estimation of Time Delay. IEEE Trans. on Acoustics, Speech, and Signal Processing, ASSP-24(1976), 320–327.

    Google Scholar 

  38. Kreuzer, E.: Numerische Untersuchung nichtlinearer dynamischer Systeme. Springer, Berlin 1987.

    Book  MATH  Google Scholar 

  39. Kühlert, K.-H.: Numerische Berechnung des Ljapunov-Spektrums. University of Hannover, Germany, Institute of Mechanics, Studienarbeit, 1989.

    Google Scholar 

  40. Lichtenberg, A.J., Lieberman, M.A.: Regular and Stochastic Motion, Appl. Math. Sciences 38, Springer, New York, 1983.

    Google Scholar 

  41. Liebert, W.; Schuster, H.G.: Proper Choice of the Time Delay for the Analysis of Chaotic Time Series. Physics Letters A, Vol. 142, 1989, 107–111.

    Article  MathSciNet  ADS  Google Scholar 

  42. Liebert, W.; Pawelzik, K.; Schuster, H.G.: Optimal Embeddings of Chaotic Attractors from Topological Considerations. Europhysics Letters, Vol. 14, 1991, 521–526.

    Article  MathSciNet  ADS  Google Scholar 

  43. Meijaard, J. P.: Dynamics of Mechanical Systems. Ph.D. Thesis, Technical University Delft, 1991.

    Google Scholar 

  44. Moon, F. C.; Shaw, S. W.: Chaotic Vibrations of a Beam With Nonlinear Bounding Excitations. Int. J. Non-Linear Mechanics 18, 1983, 465–477.

    Article  MathSciNet  ADS  Google Scholar 

  45. Moon, F.C.: Chaotic Vibrations, an Introduction for Applied Scientists and Engineers. John Wiley Sons, New York, 1987.

    MATH  Google Scholar 

  46. Müller, P.C., Bajkowski, J.; Kisljakov, S.D.: Model Based Calculation of Lyapunov Exponents for Dynamic Systems with Discontinuities. 2nd Polish-German Workshop on Dynamical Problems in Mechanical Systems, March 1017, Paderborn/Germany, 1991.

    Google Scholar 

  47. Müller, P.C.,; Bajkowski, J.; Söffker, D.: Chaotic Motions and Fault Detection in a Cracked Rotor. To appear in Nonlinear Dynamics, 1992.

    Google Scholar 

  48. Nuttall, A.H.: Some Windows with Very Good Sidelobe Behavior. IEEE Trans. on Acoustics, Speech, and Signal Processing, ASSP -29(1981), 84–91.

    Google Scholar 

  49. Oppenheim, A.V.; Schafer, R.W.: Digital Signal Processing. Prentice-Hall 1975.

    Google Scholar 

  50. Oseledec, V.I.: A Multiplicative Ergodic Theorem. Lyapunov Characteristic Numbers for Dynamical Systems. Moscow Math. Soc., 1968, 197–231.

    Google Scholar 

  51. Packard, N.H.; Crutchfield, J.P.; Farmer, J.D.; Shaw, R.S.: Geometry From a Time Series. Physical Review Letters, Vol. 45, 1980, 712–716.

    Article  ADS  Google Scholar 

  52. Paidoussis, M. P., Moon, F. C.: Nonlinear and Chaotic Fluidelastic Vibrations of a Flexible Pipe Conveying Fluid. Fluids Structures 2, 1988, 567–591.

    Article  ADS  Google Scholar 

  53. Pater, A. D. de: Optimal Design of Running Gears. Vehicles System Dynamics 18, 1989, 293–299.

    Google Scholar 

  54. Pfeiffer, F.: Seltsame Attraktoren in Zahnradgetrieben. Ing.-Archiv, Vol. 58, 1988, 113–125.

    Article  Google Scholar 

  55. Popp, K., Stelter, P.: Nonlinear Oscillations of Structures Induced by Dry Friction. In Schiehlen, W.O. (ed.), Nonlinear Dynamics in Engineering Systems. Springer, Berlin, 1990.

    Google Scholar 

  56. Rader, C.M.: An Improved Algorithm for High Speed Autocorrelation with Application to Spectral Estimation. IEEE Trans on Audio and Electroacoustics, Vol. AU-18(1979), 439–441.

    Google Scholar 

  57. Sano, M.; Sawada, Y.: Measurements of the Lyapunov Spectrum From Chaotic Time Series. Physical Review Letters, Vol. 55, 1985, 1082–1085.

    Article  MathSciNet  ADS  Google Scholar 

  58. Sato, S.; Sano, M.; Sawada, Y.: Practical Methods of Measuring the Largest Lyapunov Exponent in High Dimensional Chaotic Systems. Prog. of Theor. Phys., Vol. 77, 1987, 1–5.

    MathSciNet  Google Scholar 

  59. Shimida, I.; Nagashima, T.: A Numerical Approach to Ergodic Problem of Dissipative Dynamical Systems. Prog. of Theor. Phys. 61, 1979, 1605–1616.

    Google Scholar 

  60. Silverman, H.F.: An Introduction to Programming the Winograd Fourier Transform Algorithm (WFTA). IEEE Trans. on Acoustics, Speech, and Signal Processing, ASSP-25(1977), 152–165.

    Google Scholar 

  61. Söffker, D., Bajkowski, J.; Müller, P.C.: Detection of Cracks in Turbo Rotors - a New Observer Based Method. To appear in ASME Journal of Dynamic Systems, Measurements and Control, 1993.

    Google Scholar 

  62. Stelter, P.: Nichtlineare Schwingungen reibungserregter Strukturen, VDI-Fortschrittsberichte Nr. 137, Reihe 11, VDI-Verlag, Düsseldorf, 1990.

    Google Scholar 

  63. Stoop, R.; Parisi, J.: Calculation of Lyapunov Exponents Avoiding Spurious Elements. Physica D50, 1991, 89–94.

    MATH  Google Scholar 

  64. Szczygielski, W.M.: Dynamisches Verhalten eines schnell drehenden Rotors bei Anstreifvorgngen. Zürich: Diss. ETH Nr. 8094, 1986.

    Google Scholar 

  65. Takens, F.: Detecting Strange Attractors in Turbulance. In: Rand, D. O.; Young, L.-S. (eds.): Lecture Notes in Mathematics, 898, Springer, Berlin 1981, 366–381.

    Google Scholar 

  66. Welch, P.D.: The Use of the FFT for Estimation of Power Spectra: A Method Based on Averaging Over Short, Modified Periodogram. IEEE Trans. on Audio and Electroacoustic., AU-15 (1967), 70–73.

    Google Scholar 

  67. Whitney, H.: Differentiable Manifolds, Ann. Math., 37, 1936.

    Google Scholar 

  68. Wolf, A.; Swift, J.B.; Swinney, H.L.; Vastano, J.A.: Determining Ljapunov Exponents from a Time Series. Physica D16, 1985, 285–317.

    MathSciNet  MATH  Google Scholar 

Download references

Author information

Authors and Affiliations

  1. Safety Control Engineering, University of Wuppertal, Gaußstr. 20, D-5600, Wuppertal 1, Germany

    P. C. Müller & J. Bajkowski

Authors
  1. P. C. Müller
    View author publications

    You can also search for this author in PubMed Google Scholar

  2. J. Bajkowski
    View author publications

    You can also search for this author in PubMed Google Scholar

Editor information

Editors and Affiliations

  1. Institute B for Mechanics, University of Stuttgart, Stuttgart, Germany

    Werner Schiehlen

Rights and permissions

Reprints and permissions

Copyright information

© 1993 Springer Science+Business Media Dordrecht

About this chapter

Cite this chapter

Müller, P.C., Bajkowski, J. (1993). Signal Analysis in Multibody Systems. In: Schiehlen, W. (eds) Advanced Multibody System Dynamics. Solid Mechanics and Its Applications, vol 20. Springer, Dordrecht. https://doi.org/10.1007/978-94-017-0625-4_16

Download citation

  • DOI: https://doi.org/10.1007/978-94-017-0625-4_16

  • Publisher Name: Springer, Dordrecht

  • Print ISBN: 978-90-481-4253-8

  • Online ISBN: 978-94-017-0625-4

  • eBook Packages: Springer Book Archive

Publish with us

Policies and ethics

Search

Navigation