SELECTION OF MODAL BASIS FOR FLEXIBLE BODIES OF MECHANICAL SYSTEMS

Vibration normal modes and static correction modes have been previously used to model flexible bodies for dynamic analysis of mechanical systems with good efficiency. Accuracy of using these modes to model a system under different forcing conditions have not been fully investigated. The effectiveness of using each mode or their combinations to model the flexible body depends not only on the flexibility of the body but also on the applied external forces and their frequencies. This paper develops a criteria to estimate the error involved in modeling the flexible bodies using the selected mode shapes, based on the rigid body analysis. This estimate is used to determine the necessary number of modes of each type required to capture the flexibility effects within a desired accuracy. The equations of motion are derived for a planar system to illustrate the ideas involved and are applied to a slider crank example. This system is driven at different combinations of driving frequencies and loads to demonstrate the need to include different modes in the model. Results from the simulation illustrate the conditions under which different mode shapes must be included in the model.