Dynamics of a two-module vibration-driven system moving along a rough horizontal plane

A rectilinear motion of a system of two bodies connected by a spring on a rough horizontal plane is studied. The motion of the system is excited by two identical unbalanced rotors based on the respective bodies. Major attention is given to the steady-state motion. A nearly-resonant excitation mode, when the angular velocities of the rotor are close to the natural frequency of the system, is considered. A set of algebraic equations for determining an approximate value of the average steady-state velocity of the entire system is obtained for the case of small friction. It is shown that control of the steady-state motion can be provided by changing the phase shift between the rotations of the rotors and the sign of the resonant detuning measured by the difference between the angular velocity of the rotors and the natural frequency of the system. By varying the phase shift one can control the magnitude of the average velocity, and varying the detuning enables one to change the direction of the motion. This study was partly supported by the German Research Society (DFG) (projects Zi 540-12/1 and SFR 622) and the Russian Foundation for Basic Research (project 09-01-91330). An erratum to this article can be found at