Construction Of Mathematical Model On The Rail Under The Step Load In The Electromagnetic Launchers

In the beginning of the 19th, the principle of electromagnetic launch technology (EML) had already been raised. Electromagnetic launch technology has achieved a major breakthrough, and will have a wide range of application prospects in military, civil and industrial fields since 1970s. Recently, the literature studies Bernoulli—Euler beam as the model, but the model of Timoshenko beam is more realistic.In the electromagnetic launch, the rail is simplified as Timoshenko beams supported by the elastic foundation to discuss the effects of shear deformation under the step load in this paper. This paper analyzes the mathematical model and the control equation under different boundary conditions, obtain the solution using detached variable. Fatherly, in the use of Matlab software, it give the numerical example that illustrates the shear can not be ignored. It will lay a foundation for the force analysis of electromagnetic rail roundly, the establishment and solution of mathematical model.Firstly, the rail is modeled as a finite length of the elastic foundation beam model—Timoshenko beam to discus the simple beam under the boundary conditions, that is, ends of the beam are both hinged side of the situation. This paper gives the mathematical model and its control equation under the magnetic pressure. While it examines the solution of equations and the numerical example on the beam, taking advantage of detached variable, Lagrange equation, the relevant theory of mathematical analysis and Matlab software, and analyze the impact of shear correction factor on the beam.Secondly, the rail is modeled as the cantilever beam under the boundary condition, that is, the two ends of the beam are the fixed-side end and the free end. The paper also shows the mathematical model and its control equations under the step load, and examines the solution of differential equations of motion equations and the numerical example.Finally, the boundary conditions of the rail are fixed-side and hinged side. It also gives the mathematical model and its control equations under the step load, and examines the solution of differential equations of motion equations and the numerical example.