Interval eigenvalues of closed-loop systems of uncertain structures

Using the interval analysis, the vibration control problem of structures with interval parameters is discussed, which is approximated by a deterministic one. A method to solve the interval eigenvalues of the closed-loop system is presented. The expressions of the interval stiffness and interval mass matrix are developed directly from the interval parameters. With matrix perturbation and interval extension theory, the algorithm for estimating the upper and lower bounds of the interval complex eigenvalue is developed. The results are derived in terms of eigenvalues and left and right eigenvectors of the second-order systems. Two numerical examples are presented to illustrate the applications of the present method. The example 1 is used to show the applicability of the proposed method for the finite element model. The example 2 is used to show the validity of the present method by comparing the results with those obtained by the classical random perturbation method.