 |
A Koopman View on the Harmonic Balance and Hill Method
1 : Institute for Nonlinear Mechanics, University of Stuttgart
(INM)
-
Website
Institut für nichtlineare Mechanik Pfaffenwaldring 9 70569 Stuttgart -
Germany
2 : Institute for Nonlinear Mechanics, University of Stuttgart
(INM)
-
Website
* : Corresponding author
Institut für nichtlineare Mechanik Pfaffenwaldring 9 70569 Stuttgart -
Germany
The Koopman operator provides a way to approximate the dynamics of a nonlinear system by a linear time-invariant system of higher order. In this paper, we aim to study nonlinear time-periodic systems and propose a specific choice of Koopman basis functions combining the Taylor and Fourier bases. This basis allows to recover all equations necessary to perform the Harmonic Balance Method as well as the Hill analysis directly from the linear lifted dynamics. The Mathieu equation and a more general Hill equation are used to exemplify these findings.
