First order decoupling of equations of motion for multibody systems consisting of rigid and elastic bodies

Abstract

An improved method for deriving elastic generalized coordinates is considered and Kane's equations of motion for multibody systems consisting of an arbitrary number of rigid and elastic bodies are presented. The equations are in general form and are applicable for any desired holonomic system. Flexibility in choosing generalized speeds in terms of generalized coordinate derivatives in Kane's method is used. It is shown that proper choice of a congruency transformation between generalized coordinate derivatives and generalized speeds leads to first order decoupled equations of motion for holonomic multibody systems consisting of an arbitrary number of rigid and elastic bodies. In order to demonstrate the use of this method, a simple system consisting of a lumped mass, a spring and a clamped-free elastic beam is modeled