Hybrid state-space time integration in a rotating frame of reference

Abstract

A time integration algorithm is developed for the equations of motion of a flexible body in a rotating frame of reference. The equations are formulated in a hybrid state-space, formed by the local displacement components and the global velocity components. In the spatial discretization the local displacements and the global velocities are represented by the same shape functions. This leads to a simple generalization of the corresponding equations of motion in a stationary frame in which all inertial effects are represented via the classic global mass matrix. The formulation introduces two gyroscopic terms, while the centrifugal forces are represented implicitly via the hybrid state-space format. An angular momentum and energy conserving algorithm is developed, in which the angular velocity of the frame is represented by its mean value. A consistent algorithmic damping scheme is identified by applying the conservative algorithm to a decaying response, which is rendered stationary by an increasing exponential factor that compensates the decay. The algorithmic damping is implemented by introducing forward weighting of the mean values appearing in the algorithm. Numerical examples illustrate the simplicity and accuracy of the algorithm. Copyright © 2011 John Wiley & Sons, Ltd.