A passive vibration control system for the quenching of undesirable self-excited vibrations in mechanical systems is presented. The system is a Lanchester damper, attached to the main self-excited system; a van der Pol oscillator. A first-order perturbation solution shows that complete quenching of self-excited vibration is possible. The result is verified by numerical integration of the governing differential equations. Furthermore, the damper is shown to be effective in suppressing forced self-excited vibrations.

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