Small vibrations superimposed on non-linear rigid body motion

In the case of small elastic deformations in a exible multi- body system, the periodic motion of the system can be modelled as a superposition of a small linear vibration and a non-linear rigid body motion. For the small deformations this analysis re-sults in a set of linear dierential equations with periodic co-ecients. These equations give more insight in the vibration phenomena and are computationally more ecient than a direct non-linear analysis by numeric integration. The realization of the method in a program for exible multibody systems is discussed which requires, besides the determination of the periodic rigid motion, the determination of the linearized equations of motion. The periodic solutions for the linear equations are determined with a harmonic balance method, while transient solutions are obtained by averaging. The stability of the periodic solution is considered. The method is applied to a pendulum with a circular motion of its support pointand a slider-crank mechanism with exible connecting rod. A comparison is made with previous non-linear results.