Abstract
The response of hardening Duffing oscillators to coloured noise excitation is considered. It is shown that for certain combinations of excitation intensity and bandwidth the system realises multi-valued response states. Theoretical predictions of bounds in the parameter space which define regions of multiple statistical moments are supported by numerical simulation results. The effect of the occurrence and persistence of multi-level responses on the probability distribution of the peaks is also considered.
This is a preview of subscription content, log in via an institution to check access.
Similar content being viewed by others
Reference
Davies, H. G. (1983): The response and distribution of maxima of a non-linear oscillator with band limited excitation. J. Sound Vib. 90 (3), 333–339
Davies, H. G.; Nandlall, D. (1986): Phase plane for narrow band random excitation of a duffing oscillator, J. Sound Vib. 104 (2), 277–283
P. K. Koliopulos et al.: Effect of variation of input bandwidth on the response of hardening Duffing oscillators
Davies, H. G.; Rajan, S. (1986): Random superharmonic response of a duffing oscillator, J. Sound Vib.., 111 (1), 61–70
Davies, H. G.; Liu, Q. (1990): The response envelope probability density function of a duffing oscillator with Random Narrow-band excitation. J. Sound. Vib. 139 (1), 1–8
Dimentberg, M. F. (1988). Statistical dynamics of nonlinear and time-varying systems. Somerset, England: Research Studies Press
Fan, F. G.; Ahmadi, D. (1990): On loss of accuracy and non-uniqueness of solutions generated by equivalent linearization and cumulant-neglect methods. J. Sound Vib. 137 (3), 385–401
Fang, T.; Dowell, E. H. (1987): Numerical simulations of jump phenomena in stable duffing systems. Int. J. Nonlinear Mech. 22 (3), 267–274
Iyengar, R. N. (1988): Stochastic response and stability of the duffing oscillator under narrowband excitation. J. Sound. Vib. 126 (2), 255–263
Koliopulos, P. K.; Bishop, S. R. (1991): Sensitivity of multiple responses in nonlinear systems subjected to Random excitation, International Conference on Computational Engineering Science ICES-91, Melbourne, Australia, August 11–16. Proc. ICES '91, ICES Publications, pp. 529–532
Langley, R. S. (1988): An investigation of multiple solutions yielded by the equivalent linearisation method. J. Sound Vib. 127 (2), 271–281
Press, W. H.; Flannery, B. P.; Teukolsky, S. A.; Vetterling, W. T. (1989): Numerical recipes: the art of scientific computing (Fortran Version). New York: Cambridge University Press
Rajan, S.; Davies, H. G. (1988): Multiple time scaling of the response of a duffing oscillator to Narrow-band Random excitation, J. Sound Vib. 123 (3), 497–506
Richard, K.; Anand, G. V. (1983): Non-linear resonance in strings under narrow band Random excitation, Part I: Planar response and stability, J. Sound. Vib. 86 (1), 85–98
Roberts, J. B. (1983): Energy methods for non-linear systems with non-white excitation. In: Hennig, K. (ed): Proc. IUTAM Symposium on Random Vibrations and Reliability, pp. 285–294, Berlin: Akademie-Verlag
Roberts, J. B.; Spanos, P. D. (1990). Random vibration and statistical linearisation, Chichester, England: Wiley
Author information
Authors and Affiliations
Additional information
Communicated by S. N. Atluri, December 5, 1991
Rights and permissions
About this article
Cite this article
Koliopolus, P.K., Bishop, S.R. & Stefanou, G.D. Effect of variation of input banwidth on the response of hardening Duffing oscillators. Computational Mechanics 9, 405–415 (1992). https://doi.org/10.1007/BF00364006
Issue Date:
DOI: https://doi.org/10.1007/BF00364006