Fast projection systems are seen in various engineering applications, including weaponry systems. This work is concerned with the vibration of coupled gun barrel-bullet systems. The vibration of the muzzle end of a gun barrel (launching structure) is critical to shooting accuracy and launching safety. Under a rapid and repeated launching process, the launching structure may experience parametric resonance that is induced by accelerating projectiles. In this paper, a mathematical model of the coupled gun barrel-bullet is developed. In the development, the gun barrel is modeled by a cantilever beam; the projectiles are modeled as moving rigid bodies with time-varying velocities; and the dynamic coupling between the gun barrel and projectiles are described by pairs of springs and dampers. With this model, the dynamic response of the coupled system is determined through use of an extended solution domain (ESD) technique, which facilitates systematic solution of the dynamic response of the coupled beam-rigid body system. Numerical results show that parametric resonance can be induced in the launching structure, which is highly dependent on system parameters and projectile launching rate.

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