A SERIES METHOD TO ANALYZE NONLINEAR VOLTERRA SYSTEMSUNDER PERIODIC EXCITATION

摘要

For a nonlinear dynamic system that is modeled by differentialrnequations, the output response of nonlinear systemsrncan be obtained by simulating the nonlinear systems in therntime domain. It is not generally desirable to compute thernoutput response analytically considering formidable complexitiesrnthat may involve. Indeed, the results can be extremelyrncomplex even for some simple structured nonlinearrndynamic systems. However, such preference of numericalrnapproach over analytic one is not justified since thernnumerical approach provide little valuable understandingsrnof the intrinsic characteristics of the dynamic system itself.rnIn order to understand how different parts of the system,rnparameters of the model and different frequency componentsrnwithin the input interact with each other, an analyticrnapproach to the output response of nonlinear system hasrnbeen demonstrated in this article. A power series methodrnis developed to compute the output response of nonlinearrnsystems under periodic excitation based on the Volterra seriesrnexpansion theory of nonlinear systems. At the end ofrnthe article, an example has been given to demonstrate thernpotential application of the power series method.