A Series Method to Analyze Nonlinear Volterra Systems under Periodic Excitation

Shuming Chen and Stephen A. Billings


Nonlinear equations and systems, Nonlinear systems, Volterra integral equations, Frequency-response methods, Resonances


For a nonlinear dynamic system that is modeled by differential equations, the output response of nonlinear systems can be obtained by simulating the nonlinear systems in the time domain. It is not generally desirable to compute the output response analytically considering formidable complexities that may involve. Indeed, the results can be extremely complex even for some simple structured nonlinear dynamic systems. However, such preference of numerical approach over analytic one is not justified since the numerical approach provide little valuable understandings of the intrinsic characteristics of the dynamic system itself. In order to understand how different parts of the system, parameters of the model and different frequency components within the input interact with each other, an analytic approach to the output response of nonlinear system has been demonstrated in this article. A power series method is developed to compute the output response of nonlinear systems under periodic excitation based on the Volterra series expansion theory of nonlinear systems. At the end of the article, an example has been given to demonstrate the potential application of the power series method.

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