Analysis of purely harmonic vibrations in non-linear dynamic systems on the example of the non-linear degenerate system

摘要

Under loads of dynamic machine components made of composite materials an important role is played by their dissipative-elastic properties. The use of the traditional linear rheological model of the Kelvin type to describe these properties is often an oversimplification. In this paper the authors assume that the non-linear system is asymptotically stable and its response to the harmonic excitation can be described with a periodic ftinction of any form. The authors in this study presented the attempt to apply different concept to the system expressed by the ordinary third-order differential equation, which describes the vibrations of the 1.5 degrees of freedom (i.e. the degenerate system). For example the analyzed system presented in this work illustrates the way of excitation of purely harmonic vibrations as well as the way of the system identification with the use of the energy balance and power balance equations.