Dynamics of a rotating beam with intermittent contact

Abstract

A flexible beam that is attached to a rotating hub, and whose tip encounters intermittent contact with a flat rigid surface is modelled. The beam is modelled using Euler-Bernoulli beam theory. Lagrange Equations are used to develop the system governing equations of motion, impact is modelled using the momentum balance method and contact is represented via a Lagrange multiplier and Coulomb friction. The model does not allow penetration of the surface to occur by enforcing a geometric constraint throughout contact. Both flexible and rigid initial beam assumptions before impact were analyzed. The effects of angular velocity, depth of penetration and the friction coefficient were examined. A numerical algorithm is outlined and Matlab software is used to implement the procedure. The results show compliance with expected trends and they show smoother transition from unconstrained to constrained motion for the flexible initial beam configuration compared to the rigid configuration.