N ordsieck form of multirate integration method for flexible multibody dynamic analysis

Abstract

A Nordsieck form of multirate integration scheme has been proposed for flexible multibody dynamic systems of which motions are represented by large gross motion coupled with small vibration. Based on the conventional flexible multibody dynamics formulation, vibrational modal coordinates with floating reference frame and relative joint coordinates are employed to describe the motion in this research. In the multirate integration, the fast variables of the flexible multibody system are integrated with smaller stepsize, whereas the slow variables are integrated with larger stepsize. It is assumed that vibrational modal coordinates are treated as fast variables, whereas the relative joint coordinates are treated as slow variables to apply multirate integration method. A method that decomposes the equations of motion for flexible multibody systems into a fast system with flexible coordinates and a slow system with joint relative coordinates has been also proposed. The proposed multirate integration method is based on the Adams- Bashforth- Moulton predictor- corrector method and implemented in the Nordsieck vector form. The Nordsieck form of multirate integration method provides effective step-size control and at the same time, inherits the efficiency from the Adams integration method. Simulations of a flexible gun and turret system of a military tank have been carried out to show the effectiveness and efficiency of the proposed method.