Vibration characteristics and stability of a moving membrane with variable speed subjected to follower force

Abstract

Abstract In this paper, the vibration characteristics and stability of a moving membrane with variable speed subjected to follower force are studied. The vibration differential equation of the moving membrane is deduced by the D’Alembert principle. The intermediate variables of the differential equation are discretized by the Differential Quadrature Method, and the state equation with periodic coefficients is obtained.The state equation is solved by the implicit Runge-Kutta method. According to the Floquet theory, the dynamic stability region and instability region of the membrane are obtained, and the influence of the tension ratio, aspect ratio, average velocity and the follower force on the unstable region of the moving membrane are analyzed. This result provides theoretical guidance and basis for the design, manufacture and stability of the printing press.