Dynamic Characterization of Free Torsional Subsystem by Galerkin’s Approximate Method and its Correction

Abstract

Studying the diagrams of characteristics of complex subsystem of mechatronic one it has been determined that in case of approximate method the resonance frequencies cover with those which have been determined with exact method. However the values of the characteristic in other areas are different. Therefore there is the mistake of approximate method, which in case of studying the single systems does not have any influence because in resonance areas the characteristic values of the system approach to the infinity. However the difference in values of flexibility within two methods has the great influence on the result of complex systems. The main subject of deliberation was to determine the flexibility of the complex system with constant cross section using the exact and approximate that means Galerkin's method. The mechanical and/or mechatronic system composed from many mechanical subsystems having the same length and variable cross section, loaded by the focused moment was analysed. One case of attachment the complex system that means free torsional vibrating bar were examined. That why it was necessary to correct the results of approximate method. The problems presented in this paper, that means the analysis of subsystem of mechatronic and mechanical complex systems is however the introduction to the synthesis of torsional vibrating mechatronic systems with assumed frequency spectrum.