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The paper deals with a complex linear dynamic system with proportional damping, which is completed by various elements making the final system non-proportionally damped. Such effects emerge due to vibration absorbers, soil-structure interaction and other components and details. Influence of subsequently attached elements being a source of the non-proportional damping are reflected using perturbation method on the level of the first degree of a small parameter. This parameter characterizes the damping non-proportionality as the relevant perturbation. In the role of the first step the proportionally damped system is adopted. The basic system includes such a part of individual supplements to keep the proportional damping. Eigen-functions of the basic system are then used as a certain variational basis for approximate analysis of eigen-values and eigen-modes of the original system respecting non-proportionality. Wide numerical experiments have been carried out investigating interaction of eigen-modes between resonance domains. Applicability and shortcomings of proposed analytical-numerical procedures are commented. A few hints to improve the dynamic model fidelity and to reduce an effort of numerical evaluation are given. A couple of recommendations for engineering application of supplementary elements concerning their dynamic properties are indicated. Some open problems and perspectives of further development are outlined.

MODIFICATION OF MODAL PROPERTIES OF A SYSTEM WITH NON-PROPORTIONAL DAMPING DUE TO VIBRATION ABSORBERS AND SUB-SOIL INTERACTION