Periodic Response Prediction for Hybrid and Piecewise Linear Systems

This chapter presents a completely novel framework for the prediction and understanding of nonlinear system behavior. The idea is simply that all nonlinear systems can be represented as a combination of linear systems between which information is exchanged. Under harmonic excitation, the periodic responses of such hybrid systems may be easily calculated when the switching between linear systems is specified in terms of time. These time-switching hybrid systems provide a useful stepping stone to more realistic piecewise linear systems where the switching criteria are specified in terms of displacement and/or velocity. This chapter details the framework and illustrates its ability to efficiently predict the periodic responses from piecewise linear systems. The framework is also shown to be capable of predicting both stable and unstable periodic responses for conditions where jump behavior is possible. The extension of the work to continuous nonlinear systems is also briefly discussed.