The Nonlinear Vibration of Axially Moving Beam Impacted by High-Speed Moving Load

The vibration of axially moving beam and the vibration induced by moving load are two non-linear problems, which appears in the area of traffic, textile industry, weapons, spaceflights, and robots. The vibration including both of the forth two — the vibration of the axially moving beam induced by high-speed moving load is more complicated and its typical example is the gun barrel’s vibration. But the study on it is very limited, especially by the impulsive load. Most of the study is only about the uniform moving load. In this paper, the non-linear vibration of axially moving beam impacted by high-speed moving load is studied, and the gun barrel’s vibration while firing is used as the application background. Based on the analysis of the forces acted on the beam, which is impacted by high-speed moving load and its section changes with the position, the vibration differential equation is built. Then the equation is dispersed and solved with the method of Galerkin truncation. When assuming the vibration mode shape function, the beam’s axially moving is considered, and the length of the beam which changes with time is imported into the normal mode shape function. Then a new mode shape function which suit for this problem is applied. And the equation is solved using the method of Newmark-ß — a kind of step-by-step integral method, whose computing speed and precision are all comparatively high. After that the non-linear characteristic of the vibration is analyzed, such as the stability, the chaos and fork. In the end, numerical imitation is made using MATLAB program. The result shows that the method to build the vibration model of axially moving beam impacted by moving high-speed load and the method to solve the vibration equation are all rational. This study builds the basis of vibration control of the axially moving beam acted with moving high-speed load, and has some engineering and theoretic meaning.