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具有可变激励幅度和随时间变化的外部干扰的谐波激励下的杜芬型振荡器。

Duffing-type oscillator under harmonic excitation with a variable value of excitation amplitude and time-dependent external disturbances.

作者信息

Wawrzynski Wojciech

机构信息

Department of Ship Operation, Faculty of Navigation, Gdynia Maritime University, Aleja Jana Pawła II 3, 81-345, Gdynia, Poland.

出版信息

Sci Rep. 2021 Feb 3;11(1):2889. doi: 10.1038/s41598-021-82652-z.

DOI:10.1038/s41598-021-82652-z
PMID:33536632
原文链接:https://pmc.ncbi.nlm.nih.gov/articles/PMC7858595/
Abstract

For more complex nonlinear systems, where the amplitude of excitation can vary in time or where time-dependent external disturbances appear, an analysis based on the frequency response curve may be insufficient. In this paper, a new tool to analyze nonlinear dynamical systems is proposed as an extension to the frequency response curve. A new tool can be defined as the chart of bistability areas and area of unstable solutions of the analyzed system. In the paper, this tool is discussed on the basis of the classic Duffing equation. The numerical approach was used, and two systems were tested. Both systems are softening, but the values of the coefficient of nonlinearity are significantly different. Relationships between both considered systems are presented, and problems of the nonlinearity coefficient and damping influence are discussed.

摘要

对于更复杂的非线性系统，其中激励幅度可能随时间变化或出现与时间相关的外部干扰，基于频率响应曲线的分析可能并不充分。本文提出了一种分析非线性动力系统的新工具，作为对频率响应曲线的扩展。一种新工具可定义为所分析系统的双稳区域图和不稳定解区域图。本文基于经典的达芬方程对该工具进行了讨论。采用了数值方法，并对两个系统进行了测试。两个系统均为软化型，但非线性系数的值有显著差异。给出了两个所考虑系统之间的关系，并讨论了非线性系数和阻尼影响的问题。

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