A MODAL-ANALYSIS SOLUTION TECHNIQUE TO THE EQUATIONS OF MOTION FOR ELASTIC MECHANISM SYSTEMS INCLUDING THE RIGID-BODY AND ELASTIC MOTION COUPLING TERMS

This paper presents a modal analysis solution technique for the matrix equations of motion of elastic mechanism systems including the rigid- body elastic motion coupling terms and general damping. In many cases, researchers have neglected these terms because they complicate and di minish the efficiency of the solution process. This has been justified by assuming that the terms are small and do not affect the system res ponse. The results obtained using the techniques developed within show this is true for some, but not all mechanisms. The solution technique adds the rigid-body elastic motion coupling terms to the system mass, damping, and stiffness matrices thus allowing them to affect the syst em response appropriately. The resulting nonsymmetric matrices are the n rewritten in first order form allowing general damping to be include d in the analysis. Modal analysis techniques are utilized to solve for the steady-state response of the elastic mechanism system. Thus the m ethods developed in this work provide a technique for including the ri gid-body elastic motion coupling terms and general damping in the equa tions of motion while maintaining the advantage of using efficient mod al analysis techniques for finding the response of the system. A numbe r of examples are presented that establish the validity of this approa ch to the solution of the matrix equations of motion for elastic mecha nism systems. The results show that the rigid-body elastic motion coup ling terms can become significant at higher operating speeds.