Algorithm of Exact Methods Obtaining of the Solution and Dynamical Flexibilities of Subsystem of the Mechatronic system

In this paper the application of analysis of transverse vibrating subsystem of mechatronic systems by means of the exact were the main purposes of work to solve the task of assignment of frequency-modal analysis and characteristics of mechatronic system. At first the problem of analysis in the form of the one differential equation of motion of mechanical subsystem or of the set of state equations of considered mechatronic model of object has been formulated and solved. Classic method to solve this problem have been used. The considered transverse vibrating mechanical subsystems of mechatronic system are a continuous beams with constant cross-section, with free ends and/or clamped on one end. A ring transducer, which is the integral part of mechatronic system, extorted by harmonic force or voltage excitation, is assumed to be perfectly bonded to the beam surface. Parameters of the transducer have important influence on values of natural frequencies and on form of characteristics of considered mechatronic system. The poles of dynamical characteristic calculated by mathematical exact method and the Galerkin's method have approximately different or the same values; it is depended on the combination of boundary conditions of elementary beam. The results of the calculations were not only presented in mathematical form but also as a transients of examined dynamical characteristic which are function of frequency of assumed excitation. Practical implications of this work is to present the introduction to synthesis of considered class of mechanical and/or mechatronic beam-systems with a constant changeable cross-section. (© 2014 Wiley-VCH Verlag GmbH & Co. KGaA, Weinheim)