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首页> 外文期刊>International Journal of Mechanical Sciences >Accurate higher-order analytical approximate solutions to nonconservative nonlinear oscillators and application to van der Pol damped oscillators
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Accurate higher-order analytical approximate solutions to nonconservative nonlinear oscillators and application to van der Pol damped oscillators

机译：非保守非线性振荡器的精确高阶解析近似解及其在van der Pol阻尼振荡器上的应用

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摘要

In general, this paper deals with general nonlinear oscillations of a nonconservative and single degree-of-freedom system with odd nonlinearity and, in particular, it presents accurate higher-order analytical approximate solutions to van der Pol damped nonlinear oscillators having odd nonlinearity and the Rayleigh equation. By combining the linearization of the governing equation with harmonic balancing and the method of averaging, we establish accurate analytical approximate solutions for the general weakly damped nonlinear systems1 Unlike the classical harmonic balance method, simple linear algebraic equations instead of nonlinear algebraic equations are obtained upon linearization prior to harmonic balancing. The combination of these two methods results in very accurate transient response of the periodic solution. In addition and for the first time, this paper also presents a method for deducing fourth-, fifth- and higher-order linearized governing equations from the lower-order equations without the requirement of formulating the problem from the first principle. Three examples including the van der Pol damped nonlinear oscillator are presented to illustrate the excellent agreement with approximate solution using the exact frequency.
机译：总的来说，本文讨论了具有奇数非线性的非保守和单自由度系统的一般非线性振荡，特别是，它给出了具有奇数非线性和非线性的范德波尔阻尼非线性振荡器的精确高阶解析近似解。瑞利方程。通过将控制方程的线性化与谐波平衡和求平均方法相结合，我们为一般的弱阻尼非线性系统建立了精确的解析近似解1。与经典的谐波平衡法不同，线性化后得到的是简单的线性代数方程，而不是非线性代数方程在谐波平衡之前。这两种方法的组合导致周期解的非常精确的瞬态响应。另外，本文还首次提出了一种从低阶方程式推导出四阶，五阶和高阶线性化控制方程的方法，而无需根据第一原理来阐述问题。给出了包括范德波尔（Van der Pol）阻尼非线性振荡器的三个例子，以说明使用精确频率的近似解与优良的一致性。

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