Model reduction of a periodically forced slow–fast continuous piecewise linear system

In this paper, singular perturbation theory is exploited to obtain a reduced-order model of a slow– fast piecewise linear 2-DOF oscillator subjected to harmonic excitation. The nonsmooth nonlinearity of piecewise linear nature is studied in the case of bilinear damping as well as with bilinear stiffness characteristics. We propose a continuous matching of the locally invariant slow manifolds obtained in each subregion of the state space, which yields a reduced-order model of the same nature as the full dynamics. The frequencyresponse curves obtained from the full system and the reduced-order models  uggest that the proposed reduction method can capture nonlinear behaviors such as super- and subharmonic resonances.