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被动隔振体的非线性振动分析
被动隔振体的非线性振动分析
摘要：本文获得了隔振材料的结构阻尼的数学表达式；利用变形的3次多项式函数表征了隔振材料的非线性刚度；根据被动隔振体的拉格朗日原理导出了由地基振动激励的计及刚度非线性和结构阻尼的被动隔振体的非线性动力学方程；利用谐波平衡法研究了非线性动力响应，得出了非线性方程的周期解；并对解的稳定性进行了分析，得出了方程周期解的稳定和不稳定区域的分界线方程；对系统进行了频率响应分析，得出了频响方程；利用Matlab软件绘出了稳定和不稳定区域的分界线方程的曲线图和频率响应曲线图;获得了在进行隔振设计和隔振效果时应该注意的3点结论：
（1） 只有系统的参量位于稳定区范围时，才有稳定的周期解，在这个区域进行隔振效果比较好；
（2） 被动隔振的刚度非线性和材料阻尼非线性使被动隔振体的频率响应特性曲线呈硬特性效应，被动隔振体的振动除了存在 的主共振外，还存在 的超谐共振；
（3） 考虑刚度非线性和材料阻尼非线性的被动隔振体的振动产生突跳和滞后现象，当 时其振幅不1定是最大点。
关键词：隔振；结构阻尼；非线性；谐波平衡法
An Analysis on the Nonlinear Oscillation of Passive Vibration Isolator
Abstract: In this essay, the mathematical expression of vibration isolators’ structure damping has been obtained. By using the three-cubed multinomial function, a nonlinear rigidity of vibration isolator has been presented. On the ground of Lagrange Principle, meter and nonlinear rigidity prompted by ground vibration are calculated and the nonlinear kinetic formula is concluded. A research on nonlinear kinetic response has been done by using the method of harmonic balance and gets a periodic result of nonlinear formula. Through an analysis of the stability of the result, a bound equation of stable and instable periodic results of the nonlinear formula is found. A frequency response formula is drawn out by analyzing frequency response of the system. With the help of software Matlab, the curve charts of the bound equation and the frequency response are made. A conclusion as following is drawn with regard to vibration isolation plan and vibration isolation effects.
(1)Only when the parameter of the system is located in the stable bound, can a stable periodic result be attained and only in such a case can a sound effect of vibration isolation be found.
(2)The rigid nonlinearity of the passive vibration isolator and the nonlinearity of the damping make the frequency response curve of passive vibration isolator takes on a rigid characteristic. The main resonance of the passive vibration isolator can be expressed as . Apart from this, there are still superharmonic resonance, including
(3)Given the nonlinear rigidity and the nonlinearity of the damping, which may cause sudden leaps or delay in the vibration, the oscillation amplitude is not necessarily at the highest point even when
Keywords: Vibration isolation; Structural damping; Nonlinear; Method of harmonic balance
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