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https://hdl.handle.net/2440/16622
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Type: | Journal article |
Title: | Effect of external excitations on a nonlinear system with time delay |
Author: | Ji, J. Hansen, C. Li, X. |
Citation: | Nonlinear Dynamics, 2005; 41(4):385-402 |
Publisher: | Kluwer Academic Publ |
Issue Date: | 2005 |
ISSN: | 0924-090X 1573-269X |
Abstract: | The trivial equilibrium of a two-degree-of-freedom autonomous system may become unstable via a Hopf bifurcation of multiplicity two and give rise to oscillatory bifurcating solutions, due to presence of a time delay in the linear and nonlinear terms. The effect of external excitations on the dynamic behaviour of the corresponding non-autonomous system, after the Hopf bifurcation, is investigated based on the behaviour of solutions to the four-dimensional system of ordinary differential equations. The interaction between the Hopf bifurcating solutions and the high level excitations may induce a non-resonant or secondary resonance response, depending on the ratio of the frequency of bifurcating periodic motion to the frequency of external excitation. The first-order approximate periodic solutions for the non-resonant and super-harmonic resonance response are found to be in good agreement with those obtained by direct numerical integration of the delay differential equation. It is found that the non-resonant response may be either periodic or quasi-periodic. It is shown that the super-harmonic resonance response may exhibit periodic and quasi-periodic motions as well as a co-existence of two or three stable motions. © Springer 2005. |
DOI: | 10.1007/s11071-005-0418-2 |
Published version: | http://dx.doi.org/10.1007/s11071-005-0418-2 |
Appears in Collections: | Aurora harvest 2 Environment Institute publications Mechanical Engineering publications |
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