Dynamics of flexible multibody systems using virtual work and linear graphtheory

By combining linear graph theory with the principle of virtual work, a dyna mic 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 fle xible 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 includ e 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 virt ual work. The formulation has been implemented in a computer program, DynaF lex, that generates the equations of motion in symbolic form. Three example s are presented to demonstrate the application of the formulation, and to v alidate the symbolic computer implementation.