Purpose: of this paper is to analyze vibrating beam by an exact and approximate methods and to create hypergraphs of the beam in case of two methods of analysis. Design/methodology/approach: was to nominate the relevance or irrelevance between the characteristics obtained by the considered methods - especially concerning the relevance of the natural frequency-poles of beam characteristics. The main subject of the research is a continuous free beam as a subsystem of vibrating beam-system with constant cross sections. Findings: this approach is that approximate solutions fulfil all conditions for vibrating beams and can be an introduction to synthesis of these systems modelled by hypergraphs. Research limitations/implications: linear continuous flexibly vibrating free beam is considered Practical implications: of this study is mainly the introduction to synthesis of flexibly vibrating continuous beam-systems. Originality/value: of this approach is about application of approximate methods of analysis of a beam and modelling the one of transformed hypergraph.
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Purpose: of this paper is to investigate the transients of characteristics of vibrating beams obtained by the exact and approximate methods and to answer to the question – if the method can be used to nominate the characteristics of mechatronic systems. Design/methodology/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 mechanical part of mechatronic system. The main subject of the research is the continuous vibrating beam. Findings: this approach is fact, that approximate solutions fulfill all conditions for vibrating beams and some conditions only, particularly for vibrating beams as the subsystems of mechatronic systems. Research limitations/implications: is that linear continuous flexibly vibrating beam is considered. Practical implications: of this study is the main point is the analysis and the examination of flexibly vibrating discrete-continuous mechatronic systems which characteristics can be nominated with approximate methods only. Originality/value: of this approach relies on the comparison of the compatibility of the characteristics of the mechatronic and mechanical systems with demanded accuracy, nominated with approximate method.
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