A Modal Analysis Solution Technique to the Equations of Motion for Elastic Mechanism Systems Including the Rigid-Body and Elastic Motion Coupling Terms

Abstract

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 diminish the efficiency of the solution process. This has been justified by assuming that the terms are small and do not affect the system response. 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 system response appropriately. The resulting nonsymmetric matrices are then rewritten in first order form allowing general damping to be included in the analysis. Modal analysis techniques are utilized to solve for the steady-state response of the elastic mechanism system. Thus the methods developed in this work provide a technique for including the rigid-body elastic motion coupling terms and general damping in the equations of motion while maintaining the advantage of using efficient modal analysis techniques of finding the response of the system. A number of examples are presented that establish the validity of this approach to the solution of the matrix equations of motion for elastic mechanism systems. The results show that the rigid-body elastic motion coupling terms can become significant at higher operating speeds.