It is well known that transient rotordynamic analyses involve numerical integration of the equations of motion in order to study the response of the system under an applied forcing function. A common problem that arises in such simulations is the choice of step-size that needs to be used to obtain numerically stable results. Traditional numerical integration techniques such as the Runge-Kutta algorithms not only require splitting up second order differential equations as two first order equations, but also necessitate multiple integrations at each time-step, thus increasing the solution time. The Newmark-beta and Wilson-theta algorithms are some of the prevalent methods that have been used for transient simulations in rotordynamics. However, those single-step methods are only conditionally stable, and require iterations to converge to a solution at each time step, thus making it pseudosingle-step. In the more recent years, a modified form of the Rosenbrock algorithm has been proposed as a numerically stable and true single-step mathematical formulation for the integration of structural dynamics problems. In this paper, the modified Rosenbrock algorithm has been applied to a transient start-up multi-degree-of-freedom rotordynamics problem. A constant time step-size algorithm has been used for the simulations, and results of the transient analysis have been presented. The fact that a multi-degree-of-freedom system can be solved without condensation of the higher order modes makes the superior numerical damping characteristics of the algorithm become evident.

This content is only available via PDF.
You do not currently have access to this content.