多自由度振动结构的随机优化方法

多自由度振动结构的随机优化问题的求解一般要比确定性优化问题的求解复杂得多，也没有行之有效的算法．本文利用概率原理，把随机优化问题转化为等价的确定性优化问题，优化参数取作随机设计变量的均值和标准差，并把该方法应用于多自由度线性扭振系统，在得设计参数的最优均值的同时，还得到了相应的最优标准差，为工程技术人员控制结构零部件的加工精度提供了依据．算例表明该方法是有效的，随机优化的结果比确定性优化的结果好得多．同时，在算例中还讨论了随机设计参数的标准差对优化结果的影响．

STOCHASTIC OPTIMIZATION FOR VIBRATION SYSTEMS OF MUTIL-DEGREES OF FREEDOM

A pobabilistic approach to design variables optimization of vibrationsystems with mutil-degrees of freedom is presented. The proposed method is based onmathematical modelling of the system. Optimization is understood as a calculation of themean values and standard deviations and choosing of the random parameters which in thefeasible domain minimizes the objective function. Feasible domain is defined by probabilisticconstraints.The method is illustrated for the optimization of parameters of a linear torsionalsystem and applied to the design of dynamic absorbers. The optimal standard deviationsof the random design parameters can be obtained as well as the optimal mean values. These are very important in the control of manufacturing accuracies of the componentsof the structure. The numerical results are compared to those obtained by deterministicoptimization.In addition,the effects of the standard deviations of random design variableson the results of optimization are also discussed.