Eigenproperties of Nonclassically Damped MDOF Composite Systems

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 compute 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 technique over two other methods that have recently been proposed.