Abstract
This article presents an original method for evaluating thedissipative effect in SDOF systems due to the transient phenomenongenerated by time-varying forcing frequencies. The main contributionlies in the use of an event dimension, as additional dimension, andEinstein's method for highlighting and proving the existence of adamping term in the equation of the motion. The variational problem ofthe metric of a pseudo-Riemannian space gives the geodesic equations andthe equation of the motion. The application is concerned with aspring-pendulum system and the associated experimental investigationpermits validating the method proposed. The influence of the variationof the forcing frequency is highlighted using two different load cases:it is shown that the damping depends on the forcing frequency variation.
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References
Nashif, A. H., Jones, D. I. G., and Henderson, J. P., Vibration Damping, Wiley, New York, 1985.
Lalanne, M., 'Review: Modeling damping in mechanical engineering structures', Shock and Vibration Journal, accepted for publication.
Gjika, K., Dufour, R., and Ferraris, G., 'Transient response of structures on viscoelastic or elastoplastic mounts: Prediction and experiment', Journal of Sound and Vibration 198(3), 1996, 361–378.
Al Majid, A. and Dufour, R., 'A restoring force model to predict the shock responses of a structure on dry-friction mount', Mécanique Industrielle et Mécanique 51(2), 1998, 80–82 [in French].
Irretier, H. and Balashov, D., 'Transient resonance oscillations of a mechanical system with regard to non linear damping effect', in ASME Conference on Mechanical Vibration and Noise, ASME DETC'99/Vib8338, ASME, New York, 1999, CD-ROM, 5 pp.
Einstein, A., Four Conferences on the Theory of the Relativity Made to the University of Princeton, (translated from German to English by M. Solovine), Gauthier-Villars, Paris, 1971.
Einstein, A., The Theory of Relativity Restraint and General, Gauthier-Villars, Paris, 1971.
Elbaz, E., General Relativity and Gravitation, Ellipsis-Marketing, Paris, 1986.
Landau, L. and Lifchitz, E., Théorie des champs, (translated from Russian to French by S. Medvedev), Mir, Moscow, 1989.
Lumbroso, H., Relativity Resolute problems, Ediscience International, Paris, 1996.
Ougarov, V., Théorie de la relativité restreinte, (translated from Russian to French by V. Platonov), Mir, Moscow, 1974.
Thirring, W., Classical Mathematical Physics-Dynamical Systems and Fields Theory, Springer-Verlag, New York, 1997.
Woodhouse, N. M. J., Special Relativity, Springer-Verlag, Berlin, 1992.
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Al Majid, A., Dufour, R. An Event Dimension for Modeling Damping Due to Time-Varying Forcing Frequency. Nonlinear Dynamics 23, 303–318 (2000). https://doi.org/10.1023/A:1008332603290
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DOI: https://doi.org/10.1023/A:1008332603290