THE DYNAMIC ANALYSIS OF A THIN BEAM IMPACTING AGAINST A STOP OF GENERAL THREE-DIMENSIONAL GEOMETRY

Abstract

The dynamic response of the thin cantilever beam impacting against an elastic stop of general three-dimensional geometry is studied by extending the analysis procedure developed in the authors' previous work [1]. For the impulse response functions of the beam and stop required by the analysis procedure, an analytic solution is used for the beam and a finite element method solution is used for the stop. The contact area between the beam and the stop is the only parameter that has to be assumed in the procedure. While changes to this parameter result in significant changes to the estimate of the contact force, it is shown that at a point relatively far from the contact center the dynamic response is influenced only slightly by the assumed area. This may be interpreted as a dynamic version of the Saint-Venant's principle. It should be noted that fatigue failures of thin beams usually occur near the free edge, relatively far from the contact point, where the stress wave is reflected. Therefore, impact analysis of the thin beam against a three-dimensional object can be performed in a self contained manner for most practical purposes. Characteristics of the dynamic response of systems with a stop of various geometry are discussed based on numerical results.