Zhang, Y., and Harichandran, R. S. (1989). "Eigenproperties of
classically damped MDOF composite systems." Journal of Engineering
Mechanics, ASCE, 115(7), 1515-1526.
Abstract
A perturbation technique is employed to determine the eigenproperties of
structural systems composed of multi-degree-of-freedom (MDOF) primary
and MDOF secondary systems. The eigenproperties of the individual
subsystems are used to estimate those of the combined system.
Gerschgorin's discs are introduced to establish an accurate criterion to
distinguish between tuned and detuned modes. The effect of tuning and
interaction between the subsystems are considered in the analysis. For the
tuned case, the solution of a special eigenvalue problem related to the
tuned modes and a similarity transformation of the original tuned system
results in a new detuned system. High-order perturbations of the mode
shapes and frequencies are developed, and numerical results can be
obtained to any order of accuracy by evaluating the higher-order terms.
Gerschgorin's theorem provides an efficient means of evaluating the
error in the estimated eigenvalues. The proposed technique appears to be
more efficient and accurate than existing methods.