Mechanical interaction of a projectile body with a bore walls of an electromagnetic accelerator. Task problem

The vibration of the accelerator rails under the action of electromagnetic forces is considered. The armature and with it the right boundary of electromagnetic forces application moves along the barrel bore from the breach to muzzle. The rail accelerator is simply considered as a Bernoulli-Euler beam of finite length, lying on a viscoelastic foundation, with cantilever support from the side of the accelerator breech. The rail vibration is described by a differential equation in partial derivatives of the fourth order in coordinate and the second order in time. Using the eigenmode expansion method an analytical solution of the equation is obtained taking into account the change in the armature speed along the length of the barrel. Taking into account the peculiarities of the expression for natural vibration modes for this problem made it possible to simplify the calculations and take into account appropriate number of harmonics along the entire trajectory of the armature, which is difficult in the traditional application of the method, and thereby increase the accuracy of predicting the amplitude and nature of rail vibrations during the shot. The proposed approach allows testing and debugging numerical methods for solving complex problems, as well as more correctly designing the barrel of a rail accelerator.