Interval perturbation method for computing regions containing complex natural frequencies of structures

By interval mathematics, the problem on regions containing complex eigenvalues for structures with errors or uncertain but bounded parameters was studied. These parameters were described by interval numbers. The non-proportional damping structural eigenvalue problem with errors or uncertain but bounded parameters can be transformed into the generalized eigenvalue problem of interval matrices, and the complex eigenvalues are regions containing natural frequencies of structures with errors or uncertain but bounded parameters. For small errors or uncertain but bounded parameters, the interval perturbation method was presented for computing complex interval eigenvalues of the generalized interval eigenvalue problem, and the required regions containing natural frequencies of structures may be obtained.