Global Optimization Method For Computing Frequencies Of Structures With Interval Uncertain Parameters
计算具有区间参数结构的固有频率的优化方法

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.