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Dynamics and Control of a Two-degree-of-freedom Vibration-driven System

Klaus Zimmermann, Igor Zeidis, Mikhail Pivovarov
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 unbalance rotors based on the respective bodies. Major attention is given to the steady-state velocity-periodic 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 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.
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