| 阻尼和刚度项含时变参数的强非线性振动系统周期解研究 |
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| 引用本文： | 唐进元,陈思雨.阻尼和刚度项含时变参数的强非线性振动系统周期解研究[J].振动与冲击,2007,26(10):96-100. |
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| 作者姓名： | 唐进元 陈思雨 |
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| 作者单位： | 中南大学机电工程学院,长沙,410075 |
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| 基金项目： | 国家重点基础研究发展计划(973计划);国家自然科学基金;国家重点实验室基金 |
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| 摘 要： | 对一类阻尼和刚度系数均含有时变参数的强非线性系统进行了研究,针对时变阻尼项和刚度项之间的耦合作用使周期解的平均值发生漂移问题,为能够在任意参数平面范围内求出该系统的周期解,提出了一种改进的能量迭代法,给出了用改进的能量迭代法求此类强非线性系统主振动解及谐振解的过程与结果,推导出了系统主振动的幅频和相频响应方程。以主振动为例,把求得的周期解和幅频曲线与数值仿真结果进行了比较,结果表明解析解与数值解吻合良好。
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| 关 键 词： | 能量迭代法 周期解 非线性振动 |
| 修稿时间： | 2006-12-282007-03-09 |
STUDY ON PERIODIC SOLUTIONS OF STRONG NONLINEAR SYSTEMS WITH TIME-VARYING DAMPING AND STIFFNESS COEFFICIENT |
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| TANG Jin-yuan,CHEN Si-yu.STUDY ON PERIODIC SOLUTIONS OF STRONG NONLINEAR SYSTEMS WITH TIME-VARYING DAMPING AND STIFFNESS COEFFICIENT[J].Journal of Vibration and Shock,2007,26(10):96-100. |
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| Authors: | TANG Jin-yuan CHEN Si-yu |
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| Abstract: | An improved energy iterative method used to solve strong nonlinear system including time varying damping and stiffness coefficient is developed. The coupling between the time varying damping and the time-varying stiffness, which have led to fluctuation of the average value of a periodic solution, is analyzed. The method can find the periodic solution of a system with abitrary parameters. An example of solving the resonance solution of this kind of system is given. The amplitude-frequency and phase-frequency response equations of the primary resonance are deduced. The comparison between the analytic solutions and the numerical solutions proves the effectiveness of this energy iterative method. |
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| Keywords: | energy iterative method periodic solution nonlinear vibration |
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