两自由度振动系统的内部非线性共振

Q4 Physics and Astronomy Radio Physics and Radio Astronomy Pub Date : 2022-06-01 DOI:10.15407/rpra27.01.017
Y. Kornienko, L. V. Stulova, D. Masalov
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引用次数: 0

摘要

主题和目的。本文研究了一个具有两个自由度的非线性动力系统的行为,该系统的关节非线性是由自由度之间的所有非线性耦合建立的。目的是找出Krylov-Bogolyubov-Mitroposky(KBM)方法是否适用于偏微分方程组。方法和方法。用Krylov-Bogolyubov-Mitroposky方法对该问题进行了一次逼近。然后用数值方法对结果进行处理。后果用Krylov-Bogolyubov-Mitroposky方法对一个具有两个自由度和已知参数共振的机电系统进行了一次近似研究。对系统的相空间进行了描述。已经表明,所获得的解涵盖了两个自由度之间的能量周期性转移。所考虑的振荡系统与其文献中讨论的类似系统之间的区别在于,所考虑的电路是由内力而非外力参数激励的。在通过二极管连接的两个电路的类似系统中,耦合包括线性分量。在目前关注的系统中,耦合都是非线性的。结论所获得的结果对于研究具有两个自由度的振荡系统中自由度之间的内部非线性共振是有意义的,该振荡系统的联合非线性是由于自由度之间所有的非线性耦合引起的。所考虑的系统可以作为开发Krylov-Bo-golyubov-Mitropolsky方法应用于具有多自由度和小非线性的振荡系统的程序的测试示例。
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AN INTERNAL NONLINEAR RESONANCE IN AN OSCILLATION SYSTEM WITH TWO DEGREES OF FREEDOM
Subject and Purpose. The paper is concerned with the behavior of a nonlinear dynamic system that has two degrees of freedom and whose joint nonlinearity is established by all the nonlinear coupling between the degrees of freedom. The purpose is to find out if the Krylov—Bogolyubov—Mitropolsky (KBM) method is applicable to a system of partial differential equations. Methods and Methodology. The consideration of the problem is by the Krylov—Bogolyubov—Mitropolsky method in the first approximation. Then the results are treated using numerical methods. Results. An electromechanical system with two degrees of freedom and a known parametric resonance has been studied using the Krylov—Bogolyubov—Mitropolsky method in the first approximation. The phase space of the system has been described. It has been shown that the obtained solution covers an energy periodic transfer between the two degrees of freedom. The difference between the considered oscillation system and its analogs discussed in the literature lies in that the considered circuit is parametrically excited by an internal force rather than external one. In a similar system of two circuits connected through a diode, the coupling includes a linear component. In the system of present concern, the coupling is all-nonlinear. Conclusion. The obtained results are of interest for the research into internal nonlinear resonances between degrees of freedom in an oscillation system that has two degrees of freedom and whose joint nonlinearity is due to all the nonlinear coupling between the degrees of freedom. The considered system can serve a test example in the development of programs implementing the Krylov—Bo- golyubov—Mitropolsky method as applied to an oscillation system with numerous degrees of freedom and a small nonlinearity.
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来源期刊
Radio Physics and Radio Astronomy
Radio Physics and Radio Astronomy Physics and Astronomy-Physics and Astronomy (miscellaneous)
CiteScore
0.60
自引率
0.00%
发文量
18
审稿时长
8 weeks
期刊最新文献
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