Modeling Loose Joints in Elastic Structures-Variable Structure Motion Model Development

In this article, a hybrid parameter multiple body system (HPMBS) methodology is utilized to model the frictional contact/impact of a loose bolted joint between two sections of a cantilever beam undergoing planar slewing motion. In this preliminary model, a "rigid" joint is utilized which allows the members of the joint to be rigid, each attached to the elastic beam sections. Frictional contact/impact is modeled at four contact points. The contact constraints and momentum transfer are modeled on a basis of instantly applied nonholonomic constraints. The theoretical model of the variable structure dynamic system is developed in this article, while the momentum transfer equations (utilizing the concept of instantly applied nonholonomic constraints), numerical solution scheme, and experimental comparisons are presented in companion articles. The underlying theme of this work is to produce low order models of complicated nonlinear structural dynamics, specifically, frictional contact and impact in joints with clearance, based on first principles.