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Structural Engineering and Mechanics
  Volume 26, Number 2, May30 2007 , pages 163-178

Interval finite element method for complex eigenvalues of closed-loop systems with uncertain parameters
XiaoMing Zhang and Han Ding

    In practical engineering, the uncertain concept plays an important role in the control problems of the vibration structures. In this paper, based on matrix perturbation theory and interval finite element method, the closed-loop vibration control system with uncertain parameters is discussed. A new method is presented to develop an algorithm to estimate the upper and lower bounds of the real parts and imaginary parts of the complex eigenvalues of vibration control systems. The results are derived in terms of physical parameters. The present method is implemented for a vibration control system of the frame structure. To show the validity and effectiveness, we compare the numerical results obtained by the present method with those obtained by the classical random perturbation.
Key Words
    matrix perturbation method; interval finite element; stability robustness; random perturbation; uncertain closed-loop system
School of Mechanical Engineering, Shanghai Jiao Tong University, Huashan Road, Shanghai, 200030, P. R. China

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