Power spectra for deterministic chaotic dynamical systems

Melbourne, Ian; Gottwald, Georg A.

doi:10.1088/0951-7715/21/1/010

Cited by 29 publications

(27 citation statements)

References 22 publications

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“…1 (in present calculations n ¼ n max ¼ 150 while N ¼ 1350) we obtain the corresponding values of K c for a chosen value of c. Note, our choice of n max and N limits (in Eqs. 4,5) is consistent with that proposed by Gottwald and Melbourne [34,35,40]. N; n max !…”

Section: The 0-1 Testsupporting

confidence: 90%

Regular and chaotic vibration in a piezoelectric energy harvester

2015

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We examine regular and chaotic responses of a vibrational energy harvester composed of a vertical beam and a tip mass. The beam is excited horizontally by a harmonic inertial force while mechanical vibrational energy is converted to electrical power through a piezoelectric patch. The mechanical resonator can be described by single or double well potentials depending on the gravity force from the tip mass. By changing the tip mass we examine bifurcations from single well oscillations, to regular and chaotic vibrations between the potential wells. The appearance of chaotic responses in the energy harvesting system is illustrated by the bifurcation diagram, the corresponding Fourier spectra, the phase portraits, and is confirmed by the 0-1 test. The appearance of chaotic vibrations reduces the level of harvested energy.

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Section: The 0-1 Testsupporting

confidence: 90%

Regular and chaotic vibration in a piezoelectric energy harvester

2015

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“…(13) and (14)) is consistent with that proposed by Gottwald and Melbourne [40,41,46]. N, n max → ∞ but simultaneously n max should be about N/10.…”

Section: The 0-1 Testsupporting

confidence: 90%

Regular and chaotic vibration in a piezoelectric energy harvester with fractional damping

et al. 2015

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Abstract. We examine a vibrational energy harvester consisting of a mechanical resonator with a fractional damping and electrical circuit coupled by a piezoelectric converter. By comparing the bifurcation diagrams and the power output we show that the fractional order of damping changes the system response considerably and affects the power output. Various dynamic responses of the energy harvester are examined using phase trajectory, Fourier spectrum, Multi-scale entropy and 0-1 test. The numerical analysis shows that the fractionally damped energy harvesting system exhibits chaos, and periodic motion, as the fractional order changes. The observed bifurcations strongly influence the power output.

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“…Note, our choice of n max and N max limits is consistent with that proposed by Gottwald and Melbourne [45][46][47]] N max , n max → ∞ but simultaneously n max should be sufficiently large, n max ≈ N max /10 (for example n = n max = 135 while N = N max = 1350).…”

Section: Application Of the "0-1 Test"supporting

confidence: 75%

Dynamics of a vibrational energy harvester with a bistable beam: voltage response identification by multiscale entropy and “0-1” test

et al. 2016

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Abstract. The use of bistable laminates is a potential approach to realize broadband piezoelectric-based energy harvesting by introducing elastic non-linearities to the system. In this paper the dynamic response of a piezoelectric material attached to a bistable laminate beam is examined based on the experimental measurement of the generated voltage-time series. The system was subjected to harmonic excitations and exhibited single-well and snap-through vibrations of both periodic and chaotic character. The ability to identify the vibration modes of the energy harvester is important since different levels of power are expected in each dynamic mode. We identify the dynamics of the selected system response using return maps, multiscale entropy, and "0-1" test. The potential of the approaches to identify periodic and chaotic modes and snap-through events in the non-linear bistable harvester is described.

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Power spectra for deterministic chaotic dynamical systems

Cited by 29 publications

References 22 publications

Regular and chaotic vibration in a piezoelectric energy harvester

Regular and chaotic vibration in a piezoelectric energy harvester

Regular and chaotic vibration in a piezoelectric energy harvester with fractional damping

Dynamics of a vibrational energy harvester with a bistable beam: voltage response identification by multiscale entropy and “0-1” test

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