Abstract
Time delays occur in many physical systems. In particular, when automatic control is used with structural or mechanical systems, there typically exists a delay between measurement of the system state and corrective action. In this paper, non-linear vibrations are considered and a time delay is present in the damping. The system has one degree of freedom with weak quadratic and cubic non-linearities in the restoring force. Cases of external (forcing) excitation and of parametric excitation are treated. Six resonance conditions are analyzed by using the method of multiple scales, including primary, subharmonic, and superharmonic resonances. The effect of the time delay is investigated and the results are presented as plots of the steady state response amplitude versus the excitation frequency and amplitude.
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