Forced oscillations of cracked beam under the stochastic cyclic loading

•In the paper the results of simulated vibrations of cracked beam are given.•Realizations of vibration signals are obtained with using of mathematical model in the form of a system of nonlinear differential equations.•In the paper the dynamic of changes of characteristics of vibration’s deterministi...

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Bibliographic Details
Published in:Mechanical systems and signal processing 2018-05, Vol.104, p.242-263
Main Authors: Matsko, I., Javors'kyj, I., Yuzefovych, R., Zakrzewski, Z.
Format: Article
Language:English
Subjects:
Covariance
Covariance function
Crack propagation
Cracked beam
Cracks
Cyclic loads
Diagnostic indicators
Diagnostic systems
Differential equations
Forced oscillations
Mean function
Nondestructive testing
Oscillations
Periodically correlated random processes
Random processes
Spectral density
Statistical methods
Studies
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Summary:•In the paper the results of simulated vibrations of cracked beam are given.•Realizations of vibration signals are obtained with using of mathematical model in the form of a system of nonlinear differential equations.•In the paper the dynamic of changes of characteristics of vibration’s deterministic and stochastic parts are analyzed separately.•It is shown that characteristics of the stochastic part are more effective for the crack detection then characteristics of the deterministic part.•The mathematical model of the cracked beam forced oscillations is proposed.•The whole complex of statistical characteristics is estimated and analyzed within the theory of periodically correlated random processes. An analysis of forced oscillations of cracked beam using statistical methods for periodically correlated random processes is presented. The oscillation realizations are obtained on the basis of numerical solutions of differential equations of the second order, for the case when applied force is described by a sum of harmonic and stationary random process. It is established that due to crack appearance forced oscillations acquire properties of second-order periodical non-stationarity. It is shown that in a super-resonance regime covariance and spectral characteristics, which describe non-stationary structure of forced oscillations, are more sensitive to crack growth than the characteristics of the oscillation’s deterministic part. Using diagnostic indicators formed on their basis allows the detection of small cracks.
ISSN:0888-3270
1096-1216
DOI:10.1016/j.ymssp.2017.08.021