Dynamic eigenvalues analysis of structures with interval parameters using probabilistic theory

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.