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the main ones consists in the development of stochastic nonlinear models, since, as

experimental studies have shown, the force of friction is a random process. The slope

of the friction to velocity dependence is not a constant, but changes unpredictably,

which is due to the irregularity of the surface profile, its contamination, inconsistency

of the sliding movement and other factors. One of the components of the stochastic

approach is the study of the probabilistic structure of friction-induced vibrations

based on experimental data. Knowledge of such a structure is necessary both for

building physical and mathematical models of vibration excitations and for analyzing

the state of contact surfaces. There are many examples of such analysis in the

literature, but the main drawback of most of them is the formal use of processing

methods, which are mainly reduced to the Fourier transformation of the obtained time

sequences. Since such sequences are stochastic and may contain hidden periodicities,

as shown in this work, the results of the analysis are inconsistent. So, data processing

methods should be justified based on a mathematical model that represents these

features of vibrations.

It was noted that analysis of the spectral composition of stochastic vibrations can

be carried out on the basis of the stationary approximation, the correlation function of

which is determined by time averaging. Such a function has all properties of the

correlation function of a stationary random process. Chapter gives a brief description

of this approach, and also describes the correlation-spectral properties of the

stationary narrow-band process, represented by the Rice model. The quadrature

components, which are extracting using the Hilbert transformation, as well as the

properties of a analytic signal, are analyzed.

The power spectrum of the stationary approximation of vibrations contains

information only about their spectral composition. The analysis of the time

repeatability of vibrations, both deterministic and stochastic parts, can be carried out

on the basis of their model in the form of periodically non-stationary random

processes (PNRP). The use of moment functions of the first and second orders of the

PNVP makes it possible completely characterizes the vibration properties.

the main ones consists in the development of stochastic nonlinear models, since, as

experimental studies have shown, the force of friction is a random process. The slope

of the friction to velocity dependence is not a constant, but changes unpredictably,

which is due to the irregularity of the surface profile, its contamination, inconsistency

of the sliding movement and other factors. One of the components of the stochastic

approach is the study of the probabilistic structure of friction-induced vibrations

based on experimental data. Knowledge of such a structure is necessary both for

building physical and mathematical models of vibration excitations and for analyzing

the state of contact surfaces. There are many examples of such analysis in the

literature, but the main drawback of most of them is the formal use of processing

methods, which are mainly reduced to the Fourier transformation of the obtained time

sequences. Since such sequences are stochastic and may contain hidden periodicities,

as shown in this work, the results of the analysis are inconsistent. So, data processing

methods should be justified based on a mathematical model that represents these

features of vibrations.

It was noted that analysis of the spectral composition of stochastic vibrations can

be carried out on the basis of the stationary approximation, the correlation function of

which is determined by time averaging. Such a function has all properties of the

correlation function of a stationary random process. Chapter gives a brief description

of this approach, and also describes the correlation-spectral properties of the

stationary narrow-band process, represented by the Rice model. The quadrature

components, which are extracting using the Hilbert transformation, as well as the

properties of a analytic signal, are analyzed.

The power spectrum of the stationary approximation of vibrations contains

information only about their spectral composition. The analysis of the time

repeatability of vibrations, both deterministic and stochastic parts, can be carried out

on the basis of their model in the form of periodically non-stationary random

processes (PNRP). The use of moment functions of the first and second orders of the

PNVP makes it possible completely characterizes the vibration properties.