区间参数桁架结构动力特征值分析的概率处理

Dynamic Eigenvalues Analysis of Structures with Interval Parameters Using Probabilistic Theory

将不确定桁架结构中的区间参数用随机变量来表示,对获得的广义区间特征值方程的求解方法进行了研究,提出了一种简洁的算法。此方法假定各区间参量在允许取值区间内为具有熵最大的矩形分布,各随机变量在所定义区域内均匀分布并假设它们彼此独立,将区间特征值方程的求解采用概率理论来处理,再利用随机因子算法,来确定结构动力特征值边界,并与用随机正态分布变量描述的区间求解做了比较。通过实际工程算例对本文方法的有效性进行了验证,并与其他算法进行了比较。

Solution to a generalized eigenvalues interval equation is studied by denoting the interval parameters of uncertain structure with random variables,and a concise algorithm is presented.The interval variables are supposed to be rectangle distribution with maximum entropy in allowable range,and the random variables obey a uniform distribution in its definition domain on the assumption that they are independent each other.The solution to the interval eigenvalue equations is achieved by using the probabilistic theory,and then a random factor method is applied to obtain the bounds of eigenvalues.For comparisons,the interval variables are also supposed to be random normal distribution and the ranges of corresponding eigenvalues are obtained.Finally,an engineering practice is employed to confirm the feasibility and validity of the approach.