计算具有区间参数结构的固有频率的优化方法

GLOBAL OPTIMIZATION METHOD FOR COMPUTING FREQUENCIES OF STRUCTURES WITH INTERVAL UNCERTAIN PARAMETERS

基于区间函数的单向包含性质,把具有区间非确定参数结构的固有频率所在区间范围问题转化成两个全局优化问题,并采用一种实数编码遗传算法求取问题的全局解.用一种能够求得剪切型结构和弹簧质量系统特征值范围精确解的单调分析方法进行检验.在一些文献中,直接采用区间数运算法则和有限元法得到结构区间刚度阵和区间质量阵,并把关于该区间刚度阵和区间质量阵的广义区间特征值问题的特征值区间作为待求的非确定性结构的特征值所在的区间范围,该方法易于扩大问题的解域.算例表明,可望得到结构固有频率区间范围的准确解.

Based on the inclusion monotone property of interval functions, a global optimization method is proposed to compute the upper and lower bounds of the natural frequencies of uncertain structures. Two computational models are presented, in which the interaction among uncertain parameters in the stiffness matrix and the mass matrix was neglected or taken into consideration respectively. A real code genetic algorithm is used to solve these optimization models. A monotone analysis method, which can obtain the exact frequencies' intervals of shear-frame structures and multi-mass-spring systems, is introduced to illustrate the effectiveness of the proposed method. Numerical examples showed that the interaction among the uncertain parameters in the stiffness matrix and the mass matrix should be taken into consideration and the results of interval perturbation method could be improved distinctly. The method to form the interval stiffness matrix and the interval mass matrix firstly and then consider the eigenvalues' intervals of the general interval matrix eigenvalue problem about the obtained interval matrices as the solution of the uncertain structures may enlarge the solution domain of the original problem.