Modeling Loose Joints in Elastic Structures— Momentum Transfer Model Development

Abstract

This is the second article in a sequence of four companion articles. In these articles, a hybrid parameter multiple body system methodology is utilized to model the frictional contact/impact of a loose bolted joint between two sections of an elastic 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 one of the elastic beam sections. Frictional contact/impact is modeled at four contact points. The contact constraints and momentum transfer are modeled using the idea of instantly applied nonholonomic constraints. The momentum transfer equations will be developed herein. A review of the theoretical development is presented, followed by a step by step outline of the process. The novelty of the approach is the use of pseudo-speeds to realize the momentum transfer during the contact and impact events. The dynamical equations, numerical solution scheme, and experimental comparisons are presented in the companion articles. The motivation for this work is to produce low order models, based on first principles, of nonlinear structural phenomena, especially those associated with loose joints.