Improved Craig–Bampton Method Implemented into Durability Analysis of Flexible Multibody Systems

Abstract

The Craig–Bampton method is frequently applied in most commercial multibody dynamic software. Nevertheless, the Craig–Bampton modes only represent the free-free modes in flexible multibody systems. However, the free-free modes are incapable of all engineering applications. Hence, a rational set of reference conditions must be correctly chosen to define a unique displacement field. Firstly, a simple 2D beam with two revolute joints is taken as an example to prove that the free-free modes are not suitable for all engineering applications, and the results are validated by ANSYS and the analytical solution. Secondly, the Craig–Bampton method is improved by two different methods: (i) the reference conditions are added to the original Craig–Bampton matrix and (ii) the reference conditions are applied to the shape functions to redefine the mass and stiffness matrices before constructing the original Craig–Bampton matrix. This implementation illustrates that the improved Craig–Bampton matrix can not only generate the free-free modes but is also suitable for the non-free-free modes. Finally, two discrepant reference conditions are imposed to obtain the dynamic response of the flexible connecting rod based on the improved Craig–Bampton method, which is validated using the normal mode approach. Simulations show that the improved Craig–Bampton method can be used as a general-purpose method in durability analysis.