Statistical Linearization Analysis of Random Response of Wire-cable Isolator System
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摘要: 针对钢丝绳隔振器非线性系统随机响应运动方程求解困难、计算效率低的问题，提出钢丝绳隔振器-质量块非线性系统随机响应特性的统计线性化分析方法，并通过等效前后数值仿真进行了有效性验证，同时计算位移传递率评估钢丝绳隔振器的隔振效果。结果表明，统计线性化分析方法和数值仿真所得系统的随机响应曲线一致，验证了统计线性化分析钢丝绳隔振器系统随机响应特性的有效性和准确性，且分析速度远远高于数值仿真，显著提高了非线性隔振系统的设计效率。Abstract: In view of the difficulty and low calculation efficiency in analyzing the random response of the nonlinear system of the wire-cable vibration isolator, a statistical linearization analysis method for the random response characteristics of the nonlinear system of wire-cable isolator was proposed, and the numerical simulation was carried out to verify the effectiveness of the method. Simultaneously the displacement transfer rate was calculated to evaluate the vibration isolation effect of the wire-cable isolator. Research indicated that the results of the proposed method are consistent with the numerical simulation, and it can be used to analyze the random response accurately and effectively. Moreover, the proposed method is more efficient than the numerical simulation, significantly improving the design efficiency of the nonlinear vibration isolation system.
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表 1 平稳高斯白噪声响应计算结果
等效参数 k11=33.2633 N/mm k12=73.5273 N/mm c21=1.7679 N/(mm/s) k22=−1.7783 N/mm 统计响应量 E(x2)=0.0024 E(xZ)=0.0038 E(x2)=0.0024 ${\rm{E}}({\dot x^2}) = 0.360\;0$ E(Z2)=0.0068 
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表 2 模型参数识别结果
模型参数 N=3，M=2 ke0 −20.7042 ke1 33.2563 ke2 1.9752 ke3 0.1254 kz0 73.5276 kz1 6.3485 kz2 −0.1424 $\rho $ 1.6471 $\sigma $ 2.4562 n 0.8457
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表 3 统计线性化后各响应量拟合优度指标
随机激励信号 响应量 RNL 白噪声 位移x 0.9613 速度v 0.9738 迟滞力Z 0.9684 有色噪声 位移x 0.9653 速度v 0.9697 迟滞力Z 0.9708
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表 4 数值仿真与统计线性化分析时间
白噪声强度P/dBW 分析时间/s 数值仿真 统计线性化 0.2 4.65 0.846 0.4 4.43 0.846 0.6 6.87 0.846 0.8 7.79 0.846 1.0 3.36 0.846
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