Dynamics of flexible multibody systems using virtual work and linear graph theory

By combining linear graph theory with the principle of virtual work, a dynamic formulation is obtained that extends graph-theoretic modelling methods to the analysis of flexible multibody systems. The system is represented by a linear graph, in which nodes represent reference frames on rigid and flexible bodies, and edges represent components that connect these frames. By selecting a spanning tree for the graph, the analyst can choose the set of coordinates appearing in the final system of equations. This set can include absolute, joint, or elastic coordinates, or some combination thereof. If desired, all non-working constraint forces and torques can be automatically eliminated from the dynamic equations by exploiting the properties of virtual work. The formulation has been implemented in a computer program, DynaFlex, that generates the equations of motion in symbolic form. Three examples are presented to demonstrate the application of the formulation, and to validate the symbolic computer implementation.