2011
IMAACA 2011 Proceeding
Modeling of Flexural Vibration of Rotating Shaft with in-span Discrete External Damping
Authors: Vikas Rastogi, Amalendu Mukherjee, Anirban Dasgupta
Abstract
This paper deals with the modeling of one-dimensional continuous systems with in-span discrete external damping. The mathematical formulation for this system is similar to an internally and externally damped rotor driven through a dissipative coupling; however the umbra-Lagrangian density contributed by external damping is different. Using such formulation, the invariance of the umbra-Lagrangian density is obtained through an extension of Noether?s theorem. The rotor shaft is modeled as a Rayleigh beam. The dynamic analysis of the rotor shaft is obtained and validated through simulation studies. Results show an interesting phenomenon of limiting behaviour of the rotor shaft with internal damping beyond certain threshold speeds, which are obtained theoretically and affirmed by simulation. The results show that regenerative energy in the rotor shaft due to internal damping is dissipated through the discrete damper as well as the dissipative coupling between drive and the rotor shaft. In such case, the excitation frequency is more, the shaft speed will not increase but the slip between drive and shaft will increase due to loading of drive.
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