A Study Of Stochastic Eigen Value Problem Of Uncertain Structures Based On The Local Average Of Random Field

In general,the material characteristic and geometrical property of the mechanical system,to a certain degree,have some randomness.In this sense,the vibration of the mechanical system should be considered as random vibration of the Parametric excitation or the random vibration of the external shock,or both of them.Up to now,one of the effective methods for dealing with the stochastic structural dynamics is the stochastic finite element method.The stochastic finite element method can be regarded as a method of combining the deterministic finite element method with the probabilistic method.The study was originally originated from the discrete random field.So far,there have been many kinds of discrete methods,and local average method is the most effective.However,the existing research fails to consider the correlation between elements well when dealing with the eigenvalue problem of the random structure.This paper mainly improves the problem in this field.In this paper,a case of a cantilever beam with variable cross-section is given,and the correlation between the elements is considered by defining the local average vector correlation matrix.A simple and practical algorithm for local average vector correlation matrix is proposed by using matrix and Kronecker product.Using the random matrix perturbation method,the formulas for the correlation matrix of the vibration mode and the natural frequency variance are derived.And through the change of the random variation of the structural parameters,the correlation between the random fluctuations of the natural frequency of every order and its correlation is analyzed..Finally,Monte Carlo simulation technique is used to control the theoretical results obtained.Through the random field by computer simulation,computing system response several times.By a large number of randomized response of sample,computing their statistics,such as the mean and variance,and the reliability of theoretical calculation is verified by comparing with the statistic of theoretical calculation.