Dynamic Behavior of a Rotor with Time-Dependent Parameters

Abstract

In this paper the dynamic behavior of a rotor with variable parameters and small nonlinearity is analyzed. Besides the linear damping, rigidity and gyroscopic force that are time-dependent, some nonlinear forces exist. They cause self-excited vibrations of the rotor. The vibration problem is solved analytically as well as numerically. A new procedure based on the Krylov-Bogolubov method is developed for solving a differential equation with a complex deflection function, time variable parameters and small nonlinearity. The asymptotic analytical solutions are in good agreement with the numerical results. For the rotor with variable parameters, the stability of th pure rotational motion is also analyzed. The direct Lyapunov stability and instability theorems are applied. The methods developed in this paper are applied to three special cases : 1. the mass of the rotor is time-dependent, 2. a linear damping force is applied. 3. a linear gyroscopic or a "cross coupling damping" force is applied.