Dynamic response of cantilevered rail guns attributed to projectile/gun interaction - Theory

An analytic approach is proposed to investigate the dynamic behavior of laboratory rail guns resulting from launching a projectile. The rail gun is modeled as a beam of finite length sitting on an elastic foundation with cantilevered support at the breech end of rails. The structural response of the rail is governed by a transient fourth-order differential equation with an extra term of elastic support (containment and insulator) subjected to a transient forcing function (a moving magnetic pressure). The complete solution of the governing equation is derived and illustrated in details. The displacement solution can be further derived to obtain strain and stress profile as well as dynamic response of the rail gun. This paper mainly reports the theoretic solution which provides a step forward to predict the dynamic behavior of rail guns.