Calculating of Deformation of Electromagnetic Launcher’s Rail using Galerkin Method

ABSTRACT: In order to deformation calculating and analysis of dynamic response, electromagnetic launcher’s rail can be modeled as a beam on elastic foundation. The beam has been supposed to be a simply supported by moving load. In this paper, the Euler beam theory is applied to build the mechanical model of electromagnetic rail gun. To analytically solve the beam equation subjected to exponential magnetic pressure, Galerkin’s method and Sturm-Liouville expansion are used. In recent researches, the Lagrange equation has been employed to calculate the deformation of beam which needs to calculate the total strain energy, the kinetic energy and the dissipation energy, while in the Galerkin’s method; mathematics operations are utilized to solve the governing equation instead of them. Results demonstrated that the elastic coefficient has quite obvious effect on the deformation of the beam while the damping coefficient and the mass of rail have not obvious effect on the deformation of the beam.