Sobol’法在非线性隔振系统灵敏度分析中的应用研究  

Application of Sobol' Method to Sensitivity Analysis of a Non-Linear Passive Vibration Isolators

作　　者：于德介[1] 李睿[1] 

机构地区：[1]湖南大学机械与汽车工程学院,长沙410082

出　　处：《振动工程学报》2004年第2期210-213,共4页Journal of Vibration Engineering

基　　金：教育部留学回国人员科研启动基金资助项目 (编号 :教外司留 2 0 0 2 - 2 4 7)

摘　　要：将基于方差的全局灵敏度分析方法—— Sobol’法引用到结构动力分析中。 Sobol’方法利用积分将函数f(x)分解成递增项之和 ,通过采样计算 f(x)总方差及各项偏方差 ,从而求得灵敏度。与目前结构动力学广泛应用的局部灵敏度分析方法相比 ,该方法具有能考虑参数的随机分布、适用于参数不同的变化范围及参数同时变化情况等特点。以线性阻尼、立方刚度的非线性被动隔振体为对象 ,用 Sobol’法计算了传递率对结构参数的一阶及总灵敏度 ,得出了软、硬弹簧和线性阻尼对传递率的影响规律 。A global sensitivity analysis method based on variance - Sobol' method is introduced for the analysis of structural dynamics. The main idea behind the Sobol method is to decompose the model function f(x) into summands of increasing dimensionality using integrals. After sampling parameters, the total variance and partial variances are obtained, then sensitivities are determined. Compared with the local sensitivity analysis approaches, which are widely used in structural dynamics, it has the following features; (1) It can incorporate the influence of the whole range of variation and the form of the probability density function of the input parameters; (2) It can evaluate the effect of one parameter while all other parameters are varying as well. The first and total sensitivity of a nonlinear vibration isolator with linear damping and cubic stiffness is carried out by Sobol method, and the fourth Rounge-Kutta numerical method is used to testify the results. The laws of the influence of damping and soft spring or rigid spring to the transmissibility are obtained. The results can be used in the optimal design of nonlinear vibration isolators.

关 键 词：非线性振动 灵敏度 隔振 传递率 sobol’法 

分 类 号：O322[理学—一般力学与力学基础] TB535[理学—力学]