具有变参数和变阻尼力的阻尼非线性系统的近似解

Rezaul Karim, Pinakee Dey, Somi Akter, M. A. Arefin, Saikh Shahjahan Miah
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引用次数: 0

摘要

二阶阻尼非线性微分方程的研究在动力系统理论的发展中具有重要意义,过阻尼过程的解的性质取决于阻尼力的性质。基于Krylov-Bogoliubov和Mitropolskii (KBM)法和谐波平衡(HB)法,提出了一种具有阻尼力的非线性微分系统的近似解和变参数阻尼非线性振动系统的近似解。应用这些方法对一个算例的求解结果进行了分析。在使用MATHEMATICA和c++作为编程语言的情况下,得到了不同初始条件下的解,并绘制了相应的图形。
本文章由计算机程序翻译,如有差异,请以英文原文为准。
APPROXIMATE SOLUTIONS OF DAMPED NON LINEAR SYSTEM WITH VARYING PARAMETER AND DAMPING FORCE
The study of second-order damped nonlinear differential equations is important in the development of the theory of dynamical systems and the behavior of the solutions of the over-damped process depends on the behavior of damping forces. We aim to develop and represent a new approximate solution of a nonlinear differential system with damping force and an approximate solution of the damped nonlinear vibrating system with a varying parameter which is based on Krylov–Bogoliubov and Mitropolskii (KBM) Method and Harmonic Balance (HB) Method. By applying these methods we solve and also analyze the finding result of an example. Moreover, the solutions are obtained for different initial conditions, and figures are plotted accordingly where MATHEMATICA and C++ are used as a programming language.
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