On the finite element dynamic analysis of flexible mechanisms

Interest has increased in the dynamic analysis of multibody interconnected flexible mechanical systems. Such systems range from robot manipulators and high-speed flexible mechanisms to the space deployable structures. A common requirement of these systems is the demand for high precision and high positioning accuracy. To ensure satisfactory performance of such systems, their dynamic behavior, including inertia coupling, must be taken into consideration in the system design. The dynamic behavior is represented by a nonlinear dynamic model comprising a mixed set of reference and local elastic coordinates. The finite element method has been employed to represent the local elastic coordinates by either a finite set of nodal coordinates or a truncated set of modal coordinates. A realistic set of modal coordinates, however, must account for the centrifugal force field resulting from component rotation. The dynamically induced stiffening effect and the corresponding modal changes are found to be significant for elastic components rotating at high speeds. Numerical results are presented to evaluate the effect of such modal changes on the dynamic response of rotating flexible members. Comparisons between solutions utilizing nodal and modal coordinates are also included.