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Dynamics and control of a two-degree-of-freedom vibration-driven system

Abstract A rectilinear motion of a system of two bodies connected by a spring on a rough horizontal plane is studied. The coefficient of friction between the bodies and the plane is assumed to be small. The motion of the system is excited by two identical unbalance rotors based on the respective bodies. Major attention is given to the steady-state velocity-periodic motion. A nearly-resonant excitation mode, for which the angular velocities of the rotor are close to the natural frequency of the system, is considered. 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.