Harichandran, R. S., and Zhang, Y. (1989). "Eigenproperties of
nonclassically damped MDOF composite systems." Journal of Engineering
Mechanics, ASCE, 115(7), 1527-1542.
Abstract
In composite systems made up of multi-degree-of-freedom (MDOF) primary
and MDOF secondary systems, the composite system is virtually always
nonclassically damped, even if the individual subsystems are classically
damped. The perturbation technique outlined in the companion paper, to
computer the eigenproperties of composite systems from those of its
subsystems, is extended here to nonclassically damped systems. The
inverse expansion of a perturbed matrix is employed to transform the
generalized eigenvalue problem corresponding to nonclassically damped
systems into a standard eigenvalue problem. Once this is done, the
perturbation scheme outlined in the companion paper may be applied with
certain modifications. Gerschgorin's discs are again used to distinguish
between tuned and detuned modes. Numerical examples are used to
illustrate the advantages of the proposed tuning criterion and analysis
techniques over two other methods that have recently been proposed.