Complex Modes in Linear Stochastic Systems

Adhikari, S.
Proceedings of the First International Conference on Vibration Engineering and Technology of Machinery (VETOMAC-I), 25-27 October, 2000, IISc - Bangalore, India.

Linear dynamic systems must generally be expected to exhibit non-proportional damping. Non-proportionally damped linear systems do not possess classical normal modes but possess complex modes. In this paper we analyze the complex modes arising in multiple degree-of-freedom non-proportionally damped discrete linear stochastic systems. Second-order statistics of the complex eigenvalues and eigenvectors are presented by assuming the randomness of the system is small so that the first-order perturbation approach is valid. The proposed method is illustrated by considering numerical example based on a linear array of damped spring-mass oscillators. It is shown that the approach can predict the statistics of eigenvalues and eigenvectors with good accuracy when compared with independent Monte Carlo simulations.

@INPROCEEDINGS{cp3,
    AUTHOR={S. Adhikari},
    TITLE={Complex modes in linear stochastic systems},
    BOOKTITLE={Proceedings of the First International Conference on
    Vibration Engineering and Technology of Machinery (VETOMAC-I)},
    YEAR={2000},
    Editor={K. Venkatraman and C. S. Manohar},
    Address={Indian Institute of Science, Bangalore, India},
    Month={October},
    Note={}
}