Hinko Wolf

Effect of smoothing piecewise-linear oscillators on their stability predictions

The effects of smoothing non-smooth function on estimation of dynamical stability of the periodic response determined in the frequency domain are considered in this paper. For that purpose, a simple single-degree-of-freedom system with piecewise-linear force-displacement relationship subjected to a harmonic force excitation is analyzed. Stability of the periodic response obtained in the frequency domain by the incremental harmonic balance method is determined by using the Floquet-Liapounov theorem. Results obtained are verified in the time domain by the method of piecing the exact solutions and Runge-Kutta integration routine.

Self-tuneable velocity feedback for active isolation of random vibrations in subcritical two degree of freedom systems

It has been previously shown that skyhook damping can be used to actively reduce vibration transmission between masses in supercritical 2 degree of freedom (dof) systems. The method is based on measuring the absolute velocity of the clean body, multiplying it by a negative gain, and feeding the result back to a force actuator reacting between the clean and the dirty body. This approach results in a broadband vibration isolation. For subcritical 2 dof systems this is normally not possible due to control stability problems. These stability problems can be mitigated by including an appropriate amount of relative damping between the clean and the dirty body in addition to the absolute damping. This approach has been referred to as blended velocity feedback. In this paper the application of the blended velocity feedback on subcritical 2 dof systems is investigated using an auto-tuning controller. An algorithm to gradually change the relative and absolute feedback gains until the active isolation performance reaches its best by applying an optimal combination of the two gains is applied. There is only one such optimal combination which minimises the kinetic energy of the clean body, and consequently the performance surface has a global minimum. Furthermore there are no local minima so a trial and error algorithm could be applied. Although in the frequency domain finding the minimum of the performance surface is straightforward, in the time domain the determining the clean body mean squared velocity can take a considerable time per step of the algorithm, such that the convergence of the trial and error algorithm can be relatively slow. It is hypothesized that more sophisticated algorithms may speed-up the convergence but this would be at cost of using a model-based approach.