Dynamic response of closed-loop system with uncertain parameters using interval finite-element method

Using the interval finite-element method, the vibration control problem of structures with interval parameters is discussed, which is approximated by a deterministic one. Based on the first-order Taylor expansion, a method to solve the interval dynamic response of the closed-loop system is presented. The expressions of the interval stiffness and interval mass matrix are developed directly with the interval parameters. With matrix perturbation and interval extension theory, the algorithm for estimating the upper and lower bounds of dynamic responses is developed. The results are derived in terms of eigenvalues and left and right eigenvectors of the second-order systems. The present method is applied to a vibration system to illustrate the application. The effect of the different levels of uncertainties of interval parameters on responses is discussed. The comparison of the present method with the classical random perturbation is given, and the numerical results show that the present method is valid when the parameter uncertainties are small compared with the corresponding mean values.