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Return time approximation in planar nonlinear systems
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DOI：10.1016/j.jsv.2021.116200.png)
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Abstract
En 中文
We present a method for the calculation of the series expansion of the exact return time/period of two-dimensional nonlinear systems. The practical applicability of the theo-rem is demonstrated through simple periodic nonlinear systems such as the Duffing oscil-lator, an oscillator with quadratic nonlinearity, the nonlinear pendulum, and an oscillator with velocity-dependent stiffness. The approximate periods are compared to series expan-sions of exact periods. The results are in accordance with the series expansion of the exact period even for the system with velocity-dependent stiffness. (c) 2021 The Authors. Published by Elsevier Ltd. This is an open access article under the CC BY-NC-ND license ( http://creativecommons.org/licenses/by-nc-nd/4.0/ )
Keywords:
Return time approximation
Period approximation
Nonlinear oscillators
Carleman linearization
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