NUMERICAL-ANALYTIC METHODS FOR ANALYZING THE DYNAMIC PROPERTIES OF MECHANICAL SYSTEMS

摘要

This article is devoted to the application of the numerical-analytic methods in the analysis and synthesis of the structural and dynamic properties of the mechanical systems. For this we use the energetic surfaces that describe the potential energy of the system in configuration space. The structural and dynamic properties of the system are defined by the ordered sets of the characteristic points. We apply fractional analysis to these sets, making it possible to evaluate their scale invariance with respect to the fractal dimension index and the similarity properties of the partial subsystems and the system as a whole. We use for the nonstationary processes the wavelet transformation, which identifies the structural characteristics of the time series in the frequency and time domains. The combined use of these methods on the basis of the systems approach makes it possible to synthesize the structural and dynamic properties of the systems with regard to the specified criteria.