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.