12. The Alternating Series Approach to Nonlinear Influence in the Frequency Domain

Understanding of nonlinear effect in the frequency domain is investigated from a novel viewpoint for the Volterra class of nonlinear systems. The system output spectrum is shown to be an alternating series with respect to some model parameters that define system nonlinearities. The output spectrum can therefore be suppressed by exploiting the alternating properties to design corresponding parameters. The concept of alternating series provides a novel insight into the nonlinear influence on system output response in the frequency domain. The sufficient (and necessary) conditions in which the output spectrum can be transformed into an alternating series are studied. To illustrate the new results, several examples are given, which investigated a single degree of freedom (SDOF) mass-spring-damper system with a cubic nonlinear damper. All these results demonstrate a novel insight into the analysis and design of nonlinearities in the frequency domain.