Exponential Damping as an Approach to Internal Hysteretic Damping of Rotor Systems: FEM Model of Timoshenko Rotating Beam with Maxwell-Weichert Damping Model

Abstract

Since material losses of many engineering materials are known to be independent on frequency, the viscous damping is not always appropriate model of damping. In the case of structures, the effect of damping is usually small far from the system resonance. Unlike the case of structures, the material damping of rotor can lead to system instability. Traditional concept of hysteretic damping introduced by complex modulus of elasticity has serious drawback of its inapplicability in the time domain. Also it is inconsistent when frequency of vibration tends to zero, what is the case of rotor undergoing synchronous forward precession. In this paper, the Maxwell-Weichert material model is used to approach hysteretic material damping of rotor systems. Presented finite element model of Timoshenko rotating beam with non-viscous internal damping with exponential kernel is suitable for time domain solutions as well as for calculation of decay rates and Campbell plots of rotor systems.