Eigenproperties of Classically Damped MDOF Composite Systems

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 effects of tuning and interaction between the subsystems are considered in the analysis. For the tuned case, the solution of a small 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.