Collection of Essential Methods Among the Beams Analysis as an Introduction into the Dynamic Reverse Task Solution of Bending Vibration within Mechatronic System

Purpose of this paper is analysis of vibrating beam by the exact and approximate methods and creating the hypergraphs of the beam in case of two methods of analysis. Approach was to nominate the relevance or irrelevance between the characteristics obtained by considered methods – especially concerning the relevance of the natural frequencies-poles of characteristics of beam. The main subject of the research is the continuous free beam as a subsystem of vibrating beam-system with constant cross sections. Findings this approach is fact, that approximate solutions fulfill all conditions for vibrating beams and can be introduction to synthesis of these systems modeled by hypergraphs. Research limitation is that linear continuous transverse vibrating free beam is considered. Practical implications of this study is the main point is the introduction to synthesis of transverse vibrating continuous beam-systems. Originality of this approach relies on application approximate methods of analysis of beam and modeling the one of transformed hypergraphs.