Wavelet-Analysis-Based Chaotic Synchronization of Vibrations of Multilayer Mechanical Structures

Krysko, Vadim A.; Yakovleva, Tatiana; Dobriyan, V.; Папкова, И. В.

doi:10.1007/s10778-014-0669-z

Cited by 6 publications

(2 citation statements)

References 14 publications

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“…Similar results were reported for plates and shells. 42,43 Below, are the results based on Morlet's mother wavelets which are most suitable for the complex analysis of the vibrations of distributed mechanical systems.…”

Section: Numerical Experimentsmentioning

confidence: 99%

Principal component analysis in the linear theory of vibrations: Continuous mechanical systems driven by different kinds of external noise

Awrejcewicz

Кrysko

Mitskievich

et al. 2020

Proceedings of the Institution of Mechanical Engineers, Part C:

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In this study, an analysis of mechanical vibrations influenced by external additive white Gaussian noise and colored noise is conducted using the principal component analysis. The principal component analysis is widely employed for encoding images in image processing, biology, economics, sociology, and political science. However, it is hereby applied to analyze nonlinear dynamics of continuous mechanical systems for the first time. A rich class of objects, including straight beams, beams on Winkler foundations and spherical shells, is investigated in the present paper. The basic differential equations are obtained based on the Bernoulli–Euler hypothesis, and solutions of the linear PDEs are analyzed by means of the principal component analysis. Results obtained with the principal component analysis are compared with those for the method of empirical modal decomposition and the wavelet-packet decomposition.

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Section: Numerical Experimentsmentioning

confidence: 99%

Principal component analysis in the linear theory of vibrations: Continuous mechanical systems driven by different kinds of external noise

Awrejcewicz

Кrysko

Mitskievich

et al. 2020

Proceedings of the Institution of Mechanical Engineers, Part C:

View full text Add to dashboard Cite

show abstract

“…Elements of bifurcation theory can be found in a number of modern studies [1,[4][5][6][7][9][10][11][12][13]. In [4], it was proposed to use variational equations with coefficients dependent on a partial solution in qualitative analysis.…”

Section: Introductionmentioning

confidence: 99%