RELIABILITY ANALYSIS OF INERTER-RUBBER VIBRATION ISOLATOR SYSTEM WITH GAP NONLINEARITY
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摘要: 大多数惯容系统的研究未考虑间隙非线性的影响，有研究表明，大间隙的产生对系统响应的影响不可忽略。该文建立了含间隙非线性的惯容-橡胶复合隔振系统的随机微分方程，基于随机非线性分析方法，推导了系统响应的统计矩，计算了系统响应的概率密度函数，利用首超可靠性分析理论求得了系统的失效概率，并分析了间隙对系统响应的统计特性及可靠性的影响。同时，也考虑了非平稳激励下间隙非线性对系统响应及可靠性的影响。结果表明，间隙值变大时，系统响应的统计矩变大，概率密度函数曲线快速发散，系统的失效概率迅速增加，这与确定性分析得到的结果不同，在设计隔振器时应当考虑间隙对系统动力可靠性的影响。Abstract: Most previous investigations on inerter did not consider effects of gap nonlinearity, however, it is demonstrated that the effects of over-large gap on system responses should not be ignored. A stochastic differential equation of inerter-rubber vibration isolator with gap nonlinearity is established in this paper, the statistical moments of system responses are derived by the stochastic nonlinear analysis method, and the probability density function is further obtained. The failure probabilities are obtained by reliability analysis, and the effects of gap on system response are analyzed. Moreover, effects of gap nonlinearity under nonstationary excitation on system responses and reliability are also considered. Results show that when the gap value increases, the statistical moment of the system response increases, the probability density function curve becomes flat, and the failure probability of the system increases rapidly, which are different from those of deterministic analysis; therefore, it is advised that the effect of gap on dynamic reliability of system should be considered in the design of vibration isolator.
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图 1 一种惯容-橡胶复合隔振器示意图
Figure 1. Schematic diagram of an inertial-rubber vibration isolator
图 3 含间隙的并联式Ⅱ型ISD隔振系统
Figure 3. The parallel type II ISD vibration isolation system with gap element
图 4 平稳高斯白噪声激励下系统响应的统计矩
Figure 4. Statistical moments of system responses under stationary Gaussian white noise
图 5 平稳高斯白噪声激励下系统位移响应的概率密度函数
Figure 5. The PDF curves of displacement response of system under stationary Gaussian white noise
图 6 平稳高斯白噪声激励下系统的失效概率
Figure 6. The failure probability of system under stationary Gaussian white noise
图 7 平稳高斯白噪声激励下系统响应统计矩与间隙的关系图
Figure 7. Relationships between statistical moments of system responses and gap under stationary Gaussian white noise excitation
图 8 平稳高斯白噪声激励下系统响应概率密度函数与间隙的关系图
Figure 8. Relationships between the PDFs of system response and gap under stationary Gaussian white noise excitation
图 9 平稳高斯白噪声激励下系统的失效概率与间隙的关系图
Figure 9. Relationships between the failure probability of system and gap under stationary Gaussian white noise excitation
图 10 非平稳高斯激励下系统响应的统计矩
Figure 10. Statistical moments of system responses under nonstationary Gaussian white noise
图 11 非平稳高斯白噪声激励下系统位移响应的概率密度函数
Figure 11. The PDF curves of displacement response of system under nonstationary Gaussian white noise
图 12 非平稳高斯白噪声激励下系统的失效概率
Figure 12. The failure probability of system under nonstationary Gaussian white noise
图 13 非平稳高斯白噪声激励下系统响应统计矩与间隙的关系图
Figure 13. Relationships between statistical moments of system responses and gap under nonstationary Gaussian white noise excitation
图 14 非平稳高斯白噪声激励下系统响应概率密度函数与间隙的关系图
Figure 14. Relationships between the PDFs of system response and gap under nonstationary Gaussian white noise excitation
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