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首页> 外文期刊>Applied Mathematical Modelling >Analytical and numerical solution to the nonlinear cubic Duffing equation: An application to electrical signal analysis of distribution lines
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Analytical and numerical solution to the nonlinear cubic Duffing equation: An application to electrical signal analysis of distribution lines

机译：非线性三次Duffing方程的解析和数值解：在配电线路电信号分析中的应用

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摘要

The Duffing oscillator represents an important model to describe mathematically the nonlinear behaviour of several phenomena occurring in physics and engineering. In this paper, analytical and numerical solutions to the nonlinear cubic Duffing equation governing the time behaviour of an electrical signal are found as a function of the magnitude and of the sign of the nonlinear parameter, of the damping parameter and for different values of the forcing term. A stability analysis of the Duffing equation in the absence of the forcing term is also performed as a function of the sign and magnitude of the nonlinear parameter. A fitting procedure of the Duffing solution to the current signal flowing in different distribution lines allows us to determine the degree of nonlinearity of the electrical signal suggesting a potential way to quantify the nonlinear behaviour of current electrical signals.
机译：Duffing振荡器是一个重要的模型，可以用数学方法描述物理学和工程学中几种现象的非线性行为。在本文中，发现了控制电信号时间行为的非线性三次Duffing方程的解析解和数值解，它是非线性参数的大小和符号，阻尼参数以及不同强迫值的函数。术语。在不存在强迫项的情况下，对Duffing方程的稳定性分析还根据非线性参数的正负号和大小进行。 Duffing解对在不同配电线路中流动的电流信号的拟合过程使我们能够确定电信号的非线性程度，从而提出了一种量化当前电信号非线性行为的潜在方法。

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  • 来源
    《Applied Mathematical Modelling》 |2016年第22期|9152-9164|共13页
  • 作者

    Roberto Zivieri; Silvano Vergura; Mario Carpentieri;

  • 作者单位

    Department of Electrical and Information Engineering, Politecnico di Bari, via E. Orabona 4, Ban 1-70125, Italy,Department of Physics and Earth Sciences and Consorzio Nazionale Interuniversitario per le Scienze Fisiche (CNISM) Unit of Ferrara, University of Ferrara, via Saragat 1, Ferrara Ⅰ-44122, Italy;

    Department of Electrical and Information Engineering, Politecnico di Bari, via E. Orabona 4, Ban 1-70125, Italy;

    Department of Electrical and Information Engineering, Politecnico di Bari, via E. Orabona 4, Ban 1-70125, Italy;

  • 收录信息 美国《科学引文索引》(SCI);美国《工程索引》(EI);
  • 原文格式 PDF
  • 正文语种 eng
  • 中图分类
  • 关键词

    Duffing equation; Jacobi elliptic functions; Elliptic functions; Fixed points; Electrical signal;

    机译：达芬方程Jacobi椭圆函数;椭圆函数;定点;电信号;

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