Modeling and Investigation of Subsystems of Mechatronic Systems by Classic and/or Unclassic Methods as an Introduction to Solution of Their Inverse Task

Abstract

The problem of analysis within the form of the one differential equation of motion within the mechanical subsystem or of the set of state equations among considered mechatronic model of object has been formulated and solved. Classic and Galerkin's methods to solve the problem presented above have been used. The considered vibrating mechanical subsystems of mechatronic system are continuous bars of circular cross-section, with free ends or clamped on one end. The poles of dynamical characteristic calculated by mathematical exact method and the Galerkin's one have approximately the same values. The results of the calculations were not only presented in mathematical form but also as the transients of examined dynamical characteristic within function of frequency of assumed excitation. This approach is different from the ones considered so far. Using classic and unclassic methods among modeling, analysis and synthesis it can be assumed that the obtained results can have great value for designers of mechatronic system. and the approximate method of analysis - Galerkin's method has been used in order to obtain the frequency -modal characteristics. The exact and Galerkin's method were used in (5) as a comparison of obtaining dynamical characteristics - dynamical flexibilities for mechatronic system. To compare the obtained dynamical characteristics - dynamical flexibilities only for mechanical transverse vibrating beam, being a parts of complex mechatronic systems, an exact method and the approximate methods were used (14-26). Frequency analysis and frequency - modal analysis have been presented in this paper for the mechanical part of mechatronic system. To achieve the aim two methods of analysis have been used - the exact and Galerkin's approximate methods.