Modified perturbation method for eigenvalues of structure with interval parameters

In overcoming the drawbacks of traditional interval perturbation method due to the unpredictable effect of ignoring higher order terms, a modified parameter perturbation method is presented to predict the eigenvalue intervals of the uncertain structures with interval parameters. In the proposed method, interval variables are used to quantitatively describe all the uncertain parameters. Different order perturbations in both eigenvalues and eigenvectors are fully considered. By retaining higher order terms, the original dynamic eigenvalue equations are transformed into interval linear equations based on the orthogonality and regularization conditions of eigenvectors. The eigenvalue ranges and corresponding eigenvectors can be approximately predicted by the parameter combinatorial approach. Compared with the Monte Carlo method, two numerical examples are given to demonstrate the accuracy and efficiency of the proposed algorithm to solve both the real eigenvalue problem and complex eigenvalue problem.