Summary
In mechanical systems nonlinear effects due to cubic stiffness and Coulomb friction are often observed. The behavior of such systems is analysed for different colored noise excitations, particularly the softening Duffing oscillator. The statistical linearization is used for obtaining mean square responses and then the mean square jump phenomenon is discussed. It is shown that the jumps can occur in the Duffing oscillator with softening stiffness. It is also shown that the softening oscillator does not exhibit stationary response for some range of the excitation bandwidth. Moreover, in this range the softening system may exhibit a nonstationary response increasing to infinity with the time. In the case of stationary responses the agreement between simulation and statistical linearization results is very good. The response of a single-degree-of-freedom spring-mass system with viscous and Coulomb friction with colored noise excitation using the technique of statistical linearization is also discussed. Further a good agreement between the simulation and analytical results is observed.
Access this chapter
Tax calculation will be finalised at checkout
Purchases are for personal use only
Preview
Unable to display preview. Download preview PDF.
Similar content being viewed by others
References
Kauderer, H.: Nichlineare Mechanik. Springer-Verlag, Berlin, 1958.
Lyon, R. et al.: Response of a hard-spring oscillator to narrow band excitation. J.Acoust. Soc. Am., 1961, 33, pp.1404 – 1411.
Roberts, J.B., Spanos P.D.: Random vibration and statistical linearization. John Wiley & Sons, N. Y., 1990
Lin, Y K.: Probabilistic theory of structural dynamics. Mc Graw-Hill, N. Y., 1967.
Müller, P. C., Popp, K., Schiehlen, W.: Berechnungsverfahren stochastischer Fahrzeugschwingungen. Ing.-Arch. 49, 1980, pp. 235–254.
Nguyen Dong Anh: Influence of different types of periodic and random perturbations on oscillating nonlinear mechanical system. Doctoral Thesis. Ukranian Acad. Sci., Institute of Math. Kiev, 1986.
N. D. Anh, R. Krause, W. Schiehlen: Statistical linerization and large excitation of nonlinear stochastic mechanical systems. Zwischenbericht 54. Institute B of Mechanics, University of Stuttgart, Stuttgart, FRG, 1990.
Richard, K., Anand, G.V.: Nonlinear resonance in strings under narrow-band random excitation. J. Sound. Vib., 1983, 86, pp. 85–98.
Müller P. C., Schiehlen, W.: Linear Vibrations. Martinus Nyhoff Publ., 1985.
Levitan E. S.: Forced oscillation of a spring-mass system having combined Coulomb and viscous damping. J. of the Acoust. Soc. of America 32, pp 1265–1269 (1960).
Author information
Authors and Affiliations
Editor information
Editors and Affiliations
Rights and permissions
Copyright information
© 1992 Springer-Verlag Berlin Heidelberg
About this paper
Cite this paper
Nguyen, D.A., Krause, R., Schiehlen, W. (1992). Statistical Linearization and Large Excitation of Nonlinear Stochastic Mechanical Systems. In: Bellomo, N., Casciati, F. (eds) Nonlinear Stochastic Mechanics. IUTAM Symposia. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-84789-9_1
Download citation
DOI: https://doi.org/10.1007/978-3-642-84789-9_1
Publisher Name: Springer, Berlin, Heidelberg
Print ISBN: 978-3-642-84791-2
Online ISBN: 978-3-642-84789-9
eBook Packages: Springer Book Archive