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To improve the harmony of work, the accuracy of positioning and rise of the operation effects of machines and industrial robots the dynamics of the mechanical structures has to be optimized. Mechanical structures with general (nonproportional) damping characteristics are dynamically analysed due to dynamic effectiveness, which can be used in the identification and estimation of dynamical behaviour of machines in the phase of design or in the phase of optimization of structures or in the detection of faults. Starting with the definition of differential equations of the kinetics of a system, over the simplification of the model, the formation of the dynamic matrix, the analytical solutions are given in the searching of eigenvalues and eigenvectors and frequency responses. A practical example is given. (Jarc)