Flexible Multibody Dynamics

Flexible multibody systems contain both rigid and elastic components and aim at applications such as lightweight and high-precision mechanical systems where the elasticity of certain bodies needs to be taken into account. Since elastic bodies are governed by PDEs, as described in the previous chapter, and rigid bodies by ODEs or DAEs, the mathematical model of a flexible multibody system is heterogeneous by nature. This chapter introduces the method of floating reference frames as standard approach for flexible multibody dynamics. The treatment of constraints is extended to this problem class, and issues related to the modeling of joints are discussed. Moreover, we cover special bodies such as beams and also touch briefly upon additional nonlinearities, the so-called geometric stiffening terms. Several examples conclude this first part of the book.