被動(dòng)隔振體的非線(xiàn)性振動(dòng)分析

被動(dòng)隔振體的非線(xiàn)性振動(dòng)分析
 
摘要：本文獲得了隔振材料的結構阻尼的數學(xué)表達式；利用變形的3次多項式函數表征了隔振材料的非線(xiàn)性剛度；根據被動(dòng)隔振體的拉格朗日原理導出了由地基振動(dòng)激勵的計及剛度非線(xiàn)性和結構阻尼的被動(dòng)隔振體的非線(xiàn)性動(dòng)力學(xué)方程；利用諧波平衡法研究了非線(xiàn)性動(dòng)力響應，得出了非線(xiàn)性方程的周期解；并對解的穩定性進(jìn)行了分析，得出了方程周期解的穩定和不穩定區域的分界線(xiàn)方程；對系統進(jìn)行了頻率響應分析，得出了頻響方程；利用Matlab軟件繪出了穩定和不穩定區域的分界線(xiàn)方程的曲線(xiàn)圖和頻率響應曲線(xiàn)圖;獲得了在進(jìn)行隔振設計和隔振效果時(shí)應該注意的3點(diǎn)結論：
（1） 只有系統的參量位于穩定區范圍時(shí)，才有穩定的周期解，在這個(gè)區域進(jìn)行隔振效果比較好；
（2） 被動(dòng)隔振的剛度非線(xiàn)性和材料阻尼非線(xiàn)性使被動(dòng)隔振體的頻率響應特性曲線(xiàn)呈硬特性效應，被動(dòng)隔振體的振動(dòng)除了存在 的主共振外，還存在 的超諧共振；
（3） 考慮剛度非線(xiàn)性和材料阻尼非線(xiàn)性的被動(dòng)隔振體的振動(dòng)產(chǎn)生突跳和滯后現象，當 時(shí)其振幅不1定是最大點(diǎn)。

關(guān)鍵詞：隔振；結構阻尼；非線(xiàn)性；諧波平衡法

 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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