Dynamic Response of Double Elastic Cantilever Beam Attributed to Variable Uniformly Distributed Load

Based on the double-layer elastic foundation beam theory, the rails and the wall plates of the electromagnetic launching device are modeled as a double-layer elastic cantilever foundation beam. After establishing the kinetic differential equation and setting the boundary condition of the cantilever beam, the displacement solution of double-layer elastic cantilever foundation beam under no load condition is obtained. Applying the Heaviside Function, the deflection equation of the upper and lower beam, the expression of the bending moment, and the stress are obtained. In the case of given motion parameters and structural parameters, the analytical solutions of the rail and the wall plate are calculated. The ANSYS numerical analysis is carried out under the same condition and the results of both solutions are in good agreement. The results can provide theoretical basis for the design of strength and stiffness of the electromagnetic launch device.