Comments on the Influence of Fractional Damping on the Nonlinear Dynamics of a Portal FrameEnergy Harvester Using Wavelet Spectrum and 0–1 Test for Chaos

Journal of Vibration Engineering & Technologies ◽

10.1007/s42417-021-00383-x ◽

2021 ◽

Author(s):

Itamar Iliuk ◽

José M. Balthazar ◽

Angelo M. Tusset ◽

Reyolando M. L. R. F. Brasil ◽

Jose R. C. Piqueira

Keyword(s):

Nonlinear Dynamics ◽

Wavelet Spectrum ◽

Fractional Damping

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ON THE WAVELET TRANSFORM APPLICATION TO A STUDY OF CHAOTIC VIBRATIONS OF THE INFINITE LENGTH FLEXIBLE PANELS DRIVEN LONGITUDINALLY

International Journal of Bifurcation and Chaos ◽

10.1142/s0218127409024803 ◽

2009 ◽

Vol 19 (10) ◽

pp. 3347-3371 ◽

Cited By ~ 9

Author(s):

J. AWREJCEWICZ ◽

A. V. KRYSKO ◽

V. SOLDATOV

Keyword(s):

Nonlinear Dynamics ◽

Lyapunov Exponent ◽

Chaotic Dynamics ◽

Wavelet Spectrum ◽

Largest Lyapunov Exponent ◽

Infinite Length ◽

Continuous Wavelets ◽

Linear Vibrations ◽

Plate Strip ◽

Flexible Panels

Both classical Fourier analysis and continuous wavelets transformation are applied to study non-linear vibrations of infinitely long flexible panels subject to longitudinal sign-changeable external load actions. First the governing PDEs are derived and then the Bubnov–Galerkin method is applied to yield 2N first order ODEs. The further used Lyapunov exponent computation is described. Transition scenarios from regular to chaotic dynamics of the being investigated plate strip are analyzed using different wavelets, and their suitability and advantages/disadvantages to nonlinear dynamics monitoring and quantifying are illustrated and discussed. A few novel results devoted to the beam nonlinear dynamics behavior are reported. In addition, links between the largest Lyapunov exponent computation and the wavelet spectrum numerical estimation are also illustrated and discussed.

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