ABSTRACT: This theoretical article continues the study of the small three-dimensional vibrations of two rigid bodies. Here, they are connected not only with elastic but also with viscous damping elements. The main task of this study is also to show how is composed the system of differential equations and how is determined the damping matrix. The Finite Element Method (FEM) is also used. The obtained finite results can be applied to making individual software programs for scientific or practical studies of varied building or machine structures. This study could also be used in seismic mechanics for constructing many dynamical models of particular importance buildings.
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