Routes to chaos in continuous mechanical systems. Part 1: Mathematical models and solution methods

Awrejcewicz, Jan; Krysko, Vadim A.; Папкова, И. В.; Krysko, Anton V.

doi:10.1016/j.chaos.2012.01.016

Cited by 49 publications

(24 citation statements)

References 13 publications

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“…The rigorous discussion of the advantages of the FDM can be found in numerous papers, including [40,41]. The shells considered in the present study Table 7 Fourier frequency power spectra, 2D wavelet spectra, It should be emphasized that in the paper [42], the authors studied the dynamics of geometrically nonlinear beams by means of employing both the FEM in the Galerkin form and the FDM.…”

Section: Discussionmentioning

confidence: 99%

Chaotic vibrations of flexible shallow axially symmetric shells

et al. 2018

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In this work, chaotic dynamics of flexible spherical axially symmetric shallow shells subjected to sinusoidal transverse load is studied with emphasis put on the vibration modes. Chaos reliability is verified and validated by solving the implemented mathematical model by partial nonlinear equations governing the dynamics of flexible spherical shells and by estimating the signs of the largest Lyapunov exponents with the help of qualitatively different approaches. It is shown how the scenario of transition of the investigated shells from regular to chaotic vibrations depends on the boundary condition. The following cases are considered: (1) movable and fixed simple supports along the shell contours, taking into account shell stiffness (Feigenbaum scenario) and shell damping (RuelleTakens-Newhouse scenario), and (2) movable clamping (regular shell vibrations). The presence of dents, the location and character of which essentially depend on the shell geometric parameters, boundary conditions, and the external load parameters, is detected in some regions of the shell surface and discussed.

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Section: Discussionmentioning

confidence: 99%

Chaotic vibrations of flexible shallow axially symmetric shells

et al. 2018

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“…In this section, all numerical simulations are based on the original Duffing vibro-impact system (15) and (16). The integral schemes in Ref.…”

Section: Numerical Simulationsmentioning

confidence: 99%

“…[13][14][15][16][17]. However, due to the discontinuousness caused by non-smooth factors, the conventional Melnikov method is not directly appropriate for NSDSs.…”

Section: Introductionmentioning

confidence: 97%

Chaotic dynamics of the vibro-impact system under bounded noise perturbation

Feng

2015

Chaos, Solitons & Fractals

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“…The theory and procedures of Lyapunov exponent calculation have been properly developed [1][2][3][4] and now Lyapunov exponents are used widely in very different fields of science, including (but not limited to) physics [5], astronomy [6], medicine [7], economy [8], etc. Due to their great efficiency Lyapunov exponents are applied to a large number of complex systems, including spatially extended ones [9][10][11][12][13][14][15]). …”

Section: Introductionmentioning

confidence: 99%