Abstract
The behaviour of a hardening Duffing oscillator subjected to narrow band random excitation is examined. The influence of possible jumps, between competing states, on the probability distribution of the response amplitude is addressed. A quasi-harmonic approximation of system behaviour is adopted which is capable of reproducing the observed concave shape of probability functions and compares well with predictions obtained via stochastic averaging techniques and with digital simulations.
Similar content being viewed by others
Rererences
Roberts, J. B., ‘Energy methods for non-linear systems with non-white excitation’, in Proceedings of the IUTAM Symposium on Random Vibrations and Reliability (Ed. Hennig, K.), Akademie-Verlag, Berlin, 1983, 285–294.
Davies, H. G. and Nandlall, D., ‘Phase plane for narrow band random excitation of a Duffing oscillator’, Journal of Sound and Vibration 104, 1986, 267–283.
Fang, T. and Dowell, E. H., ‘Numerical simulations of jump phenomena in stable Duffing systems’, International Journal of Non-Linear Mechanics 22, 1987, 267–274.
Iyengar, R. N., ‘Multiple response moments and stochastic stability of a nonlinear system’, in Stochastic Structural Dynamics (Eds. Ariaratnam, S. T., Schueller, G. I., and Elishakoff, I.), Elsevier Applied Science, London, New York, 1988, 159–172.
Roberts, J. B., ‘Multiple solutions generated by statistical linearisation and their physical significance’, International Journal of Non-Linear Mechanics 26, 1991, 945–959.
Roberts, J. B. and Spanos, P. D., ‘Stochastic averaging: an approximate method for solving random vibration problems’, International Journal of Non-Linear Mechanics 21, 1986, 111–134.
Davies, H. G. and Liu, Q., ‘The response envelope probability density function of a Duffing oscillator with random narrow-band excitation’, Journal of Sound and Vibration 139, 1990, 1–8.
Spanos, P. D., ‘ARMA algorithms for ocean wave modelling’, ASME Journal of Energy Resources Technology 105, 1983, 300–309.
Barbat, A. H. and Miquel Canet, J., Structural Response Computations in Earthquake Engineering, Pineridge Presse, Swansea, Chapter 8, 1989, 401–409.
Lennox, W. C. and Kuak, Y. C., ‘Narrow-band excitation of a nonlinear oscillator’, ASME Journal of Applied Mechanics 43, 1976, 340–344.
Dimentberg, M. F., Statistical Dynamics of Nonlinear and Time-Varying Systems, Research Studies Press Ltd, Somerset, England, Chapter 3, 1988, 356–365.
Koliopulos, P. K., Bishop, S. R., and Stefanou, G. D., ‘Response statistics of nonlinear systems under variations of excitation bandwidth’, in Computational Stochastic Mechanics (Eds. Spanos, P. D. and Brebbia, C. A.). Elsevier Applied Science, London, 1991, 335–348.
Langley, R. S., ‘On various definitions of the envelope of a random process’, Journal of Sound and Vibration 105, 1986, 503–512.
Langley, R. S., Private communication, 1991.
Author information
Authors and Affiliations
Rights and permissions
About this article
Cite this article
Koliopulos, P.K., Bishop, S.R. Quasi-harmonic analysis of the behaviour of a hardening Duffing oscillator subjected to filtered white noise. Nonlinear Dyn 4, 279–288 (1993). https://doi.org/10.1007/BF00046325
Received:
Accepted:
Issue Date:
DOI: https://doi.org/10.1007/BF00046325