Spectral Response of a Beam-Stop System Under Random Excitation

  • R. Bouc
  • M. Defilippi
Conference paper
Part of the Solid Mechanics and its Applications book series (SMIA, volume 47)


A linearization procedure to estimate the spectral response at various points of a beam-stop system is proposed. The elastic stop is replaced by a spring with stiffness depending on the amplitude of the deflection at the impact location. Performing the expectation of the spectral density function of the linear system with respect to the probability density of the response amplitude (assumed to be a random variable), an estimate of the nonlinear response spectrum is derived. The efficiency of the method is checked by comparing the results with those of numerical simulations.


Power Spectral Density Spectral Response Spectral Density Function Random Excitation Stochastic Average 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.


Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.


  1. 1.
    Miles, R.N. (1989) An approximation solution for spectral response of Duffing’s oscillator with random input, Journ al of sound and vibration 132 1, 43–49.CrossRefGoogle Scholar
  2. 2.
    Guihot, P. (1990) Analyse de la réponse de structures non-linéaires sollicitées par des sources d’excitation aléatoires, application au comportement des lignes de tuyauteries sous l’effet d’un seisme, Thèse de Doctorat de l’Université Paris VI, INSTNGoogle Scholar
  3. 3.
    Bouc, R. (1991) The power spectral density of a weakly damped strongly nonlinear random oscillation and stochastic averaging Publication du LMA: Colloque Contrôle actif Vibro-acoustique et dynamique stochastique,Marseille, ISSN 0750–7356, 127Google Scholar
  4. 4.
    Soize, C. (1991) Sur le calcul des densités spectrales des réponses stationnaires pour des systèmes dynamiques stochastiques non-linéaires Publication du LMA: Colloque Contrôle actif Vibro-acoustique et dynamique stochastique, Marseille, ISSN0750–7356, 127Google Scholar
  5. 5.
    Miles, R.N. (1993) Spectral response of a bilinear oscillator, Journal of sound and vibration 163 2, 319–326.MathSciNetzbMATHCrossRefGoogle Scholar
  6. 6.
    Bouc, R. (1994) The power spectral density of response for a strongly nonlinear random oscillator, Journal of sound and vibration 175 3, 317–331.MathSciNetzbMATHCrossRefGoogle Scholar
  7. 7.
    Fogli, M., Bressolette, P. and Bernard, P. (1994) Dynamics of the stochastic oscillator with impact. To appear in the European Journal of Mechanics.Google Scholar
  8. 8.
    Bellizzi, S. and Bouc, R. (1994) Spectral response of asymmetrical random oscillators. To appear in Probabilistic Engineering Mechanics. This paper has been also presented in the Second International Conference on Computational Stochastics Mechanics/Athens/Greece/ 12–15 June, 1994. A.A. Balkema/Rotterdam/Brookfield/1995.Google Scholar
  9. 9.
    Bellizzi, S. and Bouc, R. (1995) Spectre de puissance de systèmes non-linéaires vibrants sous sollicitations aléatoires, Second Colloque National en Calcul des Structures Giens (France), 16–19 mai, 1995. Editions Hermès, Paris.Google Scholar
  10. 10.
    Lin, S.Q. and Bapat, C.N. (1993) Extension of clearance and impact force estimation approaches to a beam-stop system, Journal of sound and vibration 163 3, 423–428.CrossRefGoogle Scholar
  11. 11.
    Nicholson, J. W. and Bergman, L. A. (1986) Free-vibration of combined dynamical system, Journal of Engineering Mechanics 112 1, 1–13.CrossRefGoogle Scholar

Copyright information

© Kluwer Academic Publishers 1996

Authors and Affiliations

  • R. Bouc
    • 1
  • M. Defilippi
    • 1
  1. 1.Laboratoire de Mécanique et d’Acoustique CNRSMarseille CedexFrance

Personalised recommendations