Geometrical solution to perturbation range of resonant frequency for flexible systems

Abstract:

The range of the lightly damped resonant frequency in the flexible system is investigated based on D-decomposition approach. In the flexible system, the resonant frequency exists in the first-order and second-order terms, making its perturbation possess a nonlinear form. In this paper, two perturbation factors are introduced to reformulate the problem as a two-dimension parameter perturbation problem. Then, a geometric algorithm based on the D-decomposition approach is developed to determine the precise robust area of the two factors. The perturbation range of the resonant frequency can be obtained as the intersection points between the boundary of this area and a specific line. Numerical examples are provided to illustrate the effectiveness of the proposed method. Meanwhile, the relationship between the perturbation range and the H∞ norm is also revealed.