Vibration control of two portal frames type shear buildings through self-synchronous dynamics of two non-ideal sources indirectly coupled

The present paper proposes a new device where it is observed the self-synchronization between two unbalanced DC motors with a limited power supply when they are indirectly coupled. The vibrating system studied consists of two portal frames type shear buildings coupled, carrying each an unbalanced DC motor. The engines are supposed to rotate in the same direction and act on each as external excitation. The dynamics investigations are done with analytical and numerical methods to achieve this purpose. The synchronous solutions are derived and their stability conditions are also explored using the averaging method. The results of this analytical investigation are confirmed later by numerical simulations. The effects of some physical parameters on the self-synchronization of DC motors are presented. The impact of the nonlinear coupling between the floors on the DC motors dynamics is also explored. The Sommerfeld effect appearing in the system is reduced by taking into account the damping coming from the environment and the coupling between the portal frame. It is observed that in-phase synchronization of the non-ideal sources assures a low amplitude of vibration in the different floors compared to opposite-phase synchronization.