A simple nonlinear system generating the self-synchronization is developed in order to clarify the occurrence mechanism of the phenomena. This system consists of two nonlinear self-excited oscillators with Coulomb friction and the stick-slip motion is generated. These two oscillators are directly coupled in series by a coil-spring and a dashpot.The self-synchronized phenomena generated in this system are investigated analytically and experimentally. The validity of the analytical model and the computational method based on the shooting method are verified by comparing the computational results and the experimental results. It is clarified that two types of the self-synchronized solutions exist in this system and the vibration patterns of the self-synchronized solutions are closely related to the undamped free vibration characteristics of the model without Coulomb friction. In addition, the differences between the occurrence mechanisms of the self-synchronized solutions are analytically confirmed by examining the energy transmission between two oscillators through the coupling element. It is also proved that the unstable regions caused by the internal resonance exist in the solution branch in which two oscillators vibrate nearly in phase.

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Self-synchronized phenomena generated in rotor-type oscillators mounted on a straight-line spring-mass system are investigated experimentally and analytically. In the present study, we examine the occurrence region and pattern of selfsynchronization in two types of coupled oscillators: rigidly coupled oscillators and elastically coupled oscillators. It is clarified that the existence regions of stable solutions are governed mainly by the linear natural frequency of each spring-mass system. The results of numerical analysis confirm that the self-synchronized solutions of the elastically coupled oscillators correspond to those of the rigidly coupled oscillators. In addition, the results obtained in the present study are compared with the previously reported results for a metronome system and a moving apparatus and the different properties of the phenomena generated in the rotor-type oscillators and the pendulum-type oscillators are shown in terms of the construction of branches of self-synchronized solution and the stability.

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