Quenching of self-excited vibrations

Stable normal-mode vibrations in engineering can be undesirable and one of the possibilities for quenching these is by embedding the oscillator in an autoparametric system by coupling to a damped oscillator. There exists the possibility of destabilizing the undesirable vibrations by a suitable tuning and choice of nonlinear coupling parameters. An additional feature is that, to make the quenching effective in the case of relaxation oscillations, one also has to deform the slow manifold by choosing appropriate coupling; this is illustrated for Rayleigh and van der Pol relaxation.