Vibration of a cantilever beam that slides axially in a rigid frictionless hole

Abstract

In 1979, Boresi and Salinas prepared a report that formulates the problem and proposes a solution procedure. The report was the result of an interest in the transient behavior of a gun barrel during recoil following firing. This research considers a cantilever beam which can move axially in and out of a rigid frictionless hole and is free to vibrate laterally outside the hole. Two Euler equations describing the lateral and axial motion of the beam are presented. A transformation of coordinates to eliminate the moving boundary, and spatial non dimensionalization are used to transform the problem into a system of two coupled non linear partial differential equations with a fixed domain. A finite element formulation provides a numerical solution to the problem.