随机边界形状的结构振动特征值

将平面连续弹性体的几何边界形状考虑为随机量，建立了描述这种连续体特征值问题的随机微分方程和边界条件。通过摄动法，将随机方程化为一系列确定的方程，并同时利用广义函数的性质，变相应的随机边界条件为确定的边界条件，用确定的有限元离散方法，推导了考虑边界形状不确定的结构振动统计特征值的近似表达。

Eigenvalues of Structures with Stochastic Boundary Shape

Regarding the boundary shape of elastic structures as random variables, stochastic equations and boundary conditions that govern eigenvalue problems are set up. Utilizing perturbation method, stochastic equations are changed to be a series of deterministic equations, In the meantime stochastic boundary conditions become deterministic boundary conditions considering characters of generalized functions. After that, the eigenvalue problems of elastic structures with stochastic boundary shape are discussed and similar expressions of statistic eigenvalues of structures with uncertain boundary shape are derived. How to obtain the solutions using finite element methods is pointed out. Compared with Monte Carlo method, the method given in this paper owns enough exaction.