Numerical scheme of locating the periodic response of non-smooth non-autonomous systems of high dimension

The paper presents a numerical scheme of locating the periodic response of high dimensional systems with non-smooth characters, such as clearances, constraints, frictions. The basic idea comes from the fact that an asymptotic stable periodic response of the system attracts its transient response and it may be extracted from the transient response somehow. The paper, thus suggests a novel iteration scheme to extrapolate the periodic response from a short time history of the transient response by curve fitting. Compared with the current schemes such as shooting, incremental harmonic balancing and their improved forms, the present scheme makes full use of the information within the transient response and the system characters so that the computational efficiency has increased by an order and the numerical convergence depending on the initial iteration has greatly improved.