区间参数振动系统的动力优化

对具有区间参数的多自由度振动系统的不确定性优化问题，提出一种新的区间优化方法．利用泰勒展开和函数的区间扩张，将区间优化问题转化为近似的确定性优化问题．该方法应用于多自由度线性扭振系统，并把区间设计变量的中值和不确定性半径取作优化参数．算例表明该方法是有效的．

DYNAMIC OPTIMIZATION FOR VIBRATION SYSTEMS WITH INTERVAL PARAMETERS

The deterministic optimization of structural behavior has been well developed for specified structural parameters and loading conditions. However, in most practical situations, the structural parameters and loads are uncertain, for example, there may be measurement inaccuracy or errors in the manufacturing process. Therefore, the concept of uncertainty plays an important role in the investigation of various engineering problems. The most common approach to problems of uncertainty is to model the structural parameters as random variables or fields. Unfortunately, probabilistic model is not the only way one could describe the uncertainty, and uncertainty does not equal randomness. Since the mid-1960s, a new method called the interval analysis has appeared. Recently, the interval analysis method has been used to deal with the static displacement and eigenvalue analysis of the uncertain structures with interval parameters. However, few papers can be found about the optimization of structures with interval parameters in engineering. Hence, it is necessary to develop an effective method to solve the optimal problems of structures with interval parameters. This paper presents an interval optimization method to solve the uncertain problems of the vibration systems with multi-degrees of freedom, where the structural characteristics are assumed to be expressed as interval parameters. Using the Taylor expansion and interval extension of functions, the interval optimization problem can be transformed into the approximate deterministic optimization one, so we can use the standard algorithm of the optimization to solve the interval optimization problem. It can be seen that, using the interval optimization method, more information for the optimal structures can be obtained, such as how the optimization results change if the uncertainties of structural parameters are imposed on the structures. The present method is implemented for a torsional vibration system. A numerical example, the optimization of a dynamic absorber with interval parameters, is given. The numerical results are compared with those obtained by the deterministic optimization method. The numerical results show that the present method is effective for dealing with the optimal problems of structures with interval parameters.