具有随机约束刚度的结构的特征值

Statistical Eigenvalues of Structures with Random Boundary Restrict Stiffness

建立了结构边界具有随机约束刚度的特征值问题的方程和边界条件 ,通过摄动法 ,将随机的微分方程和边界条件化为一组确定的微分方程和边界条件。利用有限元离散方法 ,得到了统计特征值的一阶摄动近似表达式 ,并用算例对方法进行了说明和验证。

Statistical eigenvalues of structures with random boundary restrict stiffness have been studied. First, the stochastic distributed parameter differential equations plus boundary conditions that govern the eigenvalue problems have been set up. Using perturbation method, these stochastic equations and boundary conditions have been changed as a series of deterministic differential equations and boundary conditions. Then the differential equations and boundary conditions are discretied utilizing finite element method and the one order perturbation expression of random eigenvalue considering boundary stiffness is obtained. At the end, one example is shown to illustrate the method.