  A pure frequency domain method for the computation of periodic solutions of
nonlinear ordinary differential equations (ODEs) is proposed in this study. The
method is particularly suitable for the analysis of systems that feature
distinct states, i.e. where the ODEs involve piecewise defined functions. An
event-driven scheme is used which is based on the direct calculation of the
state transition time instants between these states. An analytical formulation
of the governing nonlinear algebraic system of equations is developed for the
case of piecewise polynomial systems. Moreover, it is shown that derivatives of
the solution of up to second order can be calculated analytically, making the
method especially attractive for design studies. The methodology is applied to
several structural dynamical systems with conservative and dissipative
nonlinearities in externally excited and autonomous configurations. Great
performance and robustness of the proposed procedure was ascertained.
