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.