Stability and Bifurcation Analysis of a Modified Geometrically Nonlinear Orthotropic Jeffcott Model with Internal Damping
- Cite this article as:
- Valverde, J., Escalona, J.L., Freire, E. et al. Nonlinear Dyn (2005) 42: 137. doi:10.1007/s11071-005-2365-3
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In this paper, a modified Jeffcott model is proposed and studied in order to shed light into the dynamics of a complex system, the Short Electrodynamic Tether (SET), which is similar to an unbalanced rotor. Due to the internal damping, a geometrically linear SET model appears to be unstable as predicted by the linear rotordynamics theory. Some studies in the field of rotordynamics suggest that this instability caused by internal damping do not appear if geometric nonlinearities are taken into account in the system equations of motion. Stability and bifurcation analysis have been carried out on the modified Jeffcott model, which accounts for geometric nonlinearities, orthotropy in the shaft's cross section, and a viscous damping-based internal damping model. The stability results analytically obtained have been compared with a nonlinear multibody model by means of time simulations and good agreement has been found.