Limit cycles of non-smooth oscillators

An artificial parameter-Linstedt–Poincaré method based on the introduction of a linear stiffness term, a change of independent variable and the expansion of both the solution and the frequency of oscillation in power series of the artificial parameter, and the theory of generalized functions are used to determine the frequency of limit cycles of non-smooth oscillators. The method is applied to three non-smooth oscillators, and it is shown that the first-order approximation coincides with those obtained by means of harmonic balance and parameter-expansion techniques, whereas higher-order ones are given in terms of convergent series.