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Purpose of this paper is modeling by different category graphs and analysis of vibrating clamped - free mechatronic system by the approximate method called Galerkin’s method. Such approach considers the frequency - modal analysis and assignment of amplitude - frequence charcteristics of the mechatronic system. Design/methodology/approach: was to nominate the relevance or irrelevance between the characteristics obtained by exact - only for shaft - and considered method. Such formulation especially concerns the relevance the relevance of the natural frequencies-poles of characteristics both of mechanical subsystem and the discrete - continuous clamped - free vibrating mechatronic system. Finding this approach is a fact, that approximate solutions fulfill all conditions for vibrating mechanical and/ or mechatronic systems and can be an introduction to synthesis of these systems modeled by different category graphs. Research limitations/implications: Research limitation is that both torsional vibrating continuous mechanical subsystem and mechatronic discrete - continuous subsystems are linear discrete - continuous are linear systems. Practical implications: of this study is that the main point can be the introduction to synthesis of considered class mechatronic bar-systems with constant changeable cross-section. Originality/valut Originality of such formulation rely on the use of the hypergraph methods of modelling and synthesis of torsionally vibrating bars to the synthesis of discrete-continuous mechatronic systems.
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