Self-organization of irregular NEM vibrations in multi-mode shuttle structures

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We investigate theoretically multi-mode electromechanical "shuttle" instabilities in DC voltage-biased nanoelectromechanical single-electron tunneling (NEM-SET) devices. We show that initially irregular (quasi-periodic) oscillations, that occur as a result of the simultaneous self-excitation of several mechanical modes with incommensurable frequencies, self-organize into periodic oscillations with a frequency corresponding to the eigenfrequency of one of the unstable modes. This effect demonstrates that a local probe can selectively excite global vibrations of extended objects.