The dynamic response and bifurcations of a harmonic oscillator with a hysteretic
restoring force and sinusoidal excitation are investigated. A multilinear model
of hysteresis is presented. A hybrid system approach is used to formulate and study
the problem. A novel method for obtaining exact transient and steady state response
of the system is discussed. Simple periodic orbits of the system are analyzed using
the KBM method and an analytic criterion for existence of bound and unbound
resonance is derived. Results of KBM analysis are compared with those from numerical
simulations. Stability and bifurcations of higher period orbits are studied using
Poincar´e maps. The Poincar´e map for the system is constructed by composing the
corresponding maps for the individual subsystems of the hybrid system. The novelty
of this work lies in a.) the study of a multilinear model of hysteresis, and, b.) developing
a methodology for obtaining the exact transient and steady state response of
the system.
| Identifer | oai:union.ndltd.org:tamu.edu/oai:repository.tamu.edu:1969.1/ETD-TAMU-2856 |
| Date | 15 May 2009 |
| Creators | Shekhawat, Ashivni |
| Contributors | Kalmar-Nagy, Tamas |
| Source Sets | Texas A and M University |
| Language | en_US |
| Detected Language | English |
| Type | Book, Thesis, Electronic Thesis, text |
| Format | electronic, application/pdf, born digital |
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