A preliminary investigation into optimising the response of vibrating systems used for ultrasonic cutting

The coupling of two non-linear oscillators is investigated, each with opposing non-linear overhang characteristics in the frequency domain as a result of positive and negative cubic stiffness. This leads to the definition of a two-degree-of-freedom Duffing oscillator in which such non-linear effects can be neutralised under certain dynamic conditions. The physical motivation for this system stems from applications in ultrasonic cutting in which an exciter drives a tuned blade. The exciter and the blade are both strongly non-linear, with features strongly reminiscent of positive and negative cubic effects. It is shown by means of approximate analysis that in the case of simple idealised coupled oscillator models a practically useful mitigating effect on the overall non-linear response of the system is observed when one of the cubic stiffnesses is varied. Experimentally, it has also been demonstrated that coupling of ultrasonic components with different non-linear characteristics can strongly influence the performance of the system and that the general behaviour of the hypothetical theoretical model is indeed borne out in practice.