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Research Papers

Rotations of Pendulum When Its Pivot Oscillates Chaotically

[+] Author and Article Information
Sze-Hong Teh

Faculty of Engineering,
University of Nottingham Malaysia Campus,
Semenyih 43500, Selangor, Malaysia
e-mail: SzeHong.Teh@nottingham.edu.my

Ko-Choong Woo

Faculty of Engineering,
University of Nottingham Malaysia Campus,
Semenyih 43500, Selangor, Malaysia
e-mail: Woo.Ko-Choong@nottingham.edu.my

Hazem Demrdash

Faculty of Engineering,
University of Nottingham Malaysia Campus,
Semenyih 43500, Selangor, Malaysia
e-mail: Hazem.Demrdash@nottingham.edu.my

1Corresponding author.

Contributed by the Design Engineering Division of ASME for publication in the JOURNAL OF COMPUTATIONAL AND NONLINEAR DYNAMICS. Manuscript received December 23, 2016; final manuscript received July 29, 2017; published online October 9, 2017. Assoc. Editor: Mohammad Younis.

J. Comput. Nonlinear Dynam 13(1), 011006 (Oct 09, 2017) (11 pages) Paper No: CND-16-1637; doi: 10.1115/1.4037595 History: Received December 23, 2016; Revised July 29, 2017

This paper investigates the possibility of energy generation via pendulum rotations when the source of vertical excitation is chaotic in nature. The investigations are conducted using an additional height-adjustable mechanism housing a secondary spring to optimize a configuration of experimental pendulum setup. Chaotic oscillations of the pendulum pivot are made possible at certain excitation conditions due to a piecewise-linear stiffness characteristic introduced by the modification. A velocity control method is applied to maintain the rotational motion of the pendulum as it interacts with the vertical oscillator. The control input is affected by a motor, and a generator is used to quantify the energy extraction. The experimental results imply the feasibility of employing a pendulum device in a chaotic vibratory environment for energy harvesting purpose.

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Figures

Grahic Jump Location
Fig. 1

(a) Experimental rig for chaotic vertical excitation of pendulum and (b) some major parts of the expansion assembly

Grahic Jump Location
Fig. 2

Nonlinear restoring force as a function of vertical displacement of the pendulum assembly

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Fig. 3

Schematic of the experimental pendulum system of present work

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Fig. 4

Time history of experimental system with the proposed spring mechanism recorded for controlled rotation: (a) angular axis, (b) vertical oscillations, (c) control voltage, and (d) command signal generated to solid-state relay. It is observed at V = 130 Vrms, fctrl = 1.80 Hz.

Grahic Jump Location
Fig. 5

(a) Phase portrait of angular axis in Fig. 4, (b) amplitude spectra of vertical oscillations in Fig. 4, (c) phase portrait of vertical oscillations in Fig. 4, and (d) Poincaré section of vertical oscillations in Fig. 4

Grahic Jump Location
Fig. 6

Time history of experimental system with the proposed spring mechanism recorded for controlled rotation: (a) angular axis, (b) vertical oscillations, (c) control voltage, and (d) command signal generated to solid-state relay. It is observed at V = 130 Vrms, fctrl = 2.60 Hz.

Grahic Jump Location
Fig. 7

(a) Phase portrait of angular axis in Fig. 6, (b) amplitude spectra of vertical oscillations in Fig. 6, (c) phase portrait of vertical oscillations in Fig. 6, and (d) Poincaré section of vertical oscillations in Fig. 6

Grahic Jump Location
Fig. 8

Time history of experimental system with the proposed spring mechanism recorded for controlled rotation: (a) angular axis, (b) vertical oscillations, (c) control voltage, and (d) command signal generated to solid-state relay. It is observed at V = 130 Vrms, fctrl = 2.70 Hz.

Grahic Jump Location
Fig. 9

(a) Phase portrait of angular axis in Fig. 8, (b) amplitude spectra of vertical oscillations in Fig. 8, (c) phase portrait of vertical oscillations in Fig. 8, and (d) Poincaré section of vertical oscillations in Fig. 8

Grahic Jump Location
Fig. 10

Time history of experimental system with the proposed spring mechanism recorded for controlled rotation: (a) angular axis, (b) vertical oscillations, (c) control voltage, and (d) command signal generated to solid-state relay. It is observed at V = 130 Vrms, fctrl = 2.90 Hz.

Grahic Jump Location
Fig. 11

(a) Phase portrait of angular axis in Fig. 10, (b) amplitude spectra of vertical oscillations in Fig. 10, (c) phase portrait of vertical oscillations in Fig. 10, and (d) Poincaré section of vertical oscillations in Fig. 10

Grahic Jump Location
Fig. 12

Time history of experimental system with the proposed spring mechanism recorded for controlled rotation: (a) angular axis, (b) vertical oscillations, (c) control voltage, and (d) command signal generated to solid-state relay. It is observed at V = 130 Vrms, fctrl = 3.00 Hz.

Grahic Jump Location
Fig. 13

(a) Phase portrait of angular axis in Fig. 12, (b) amplitude spectra of vertical oscillations in Fig. 12, (c) phase portrait of vertical oscillations in Fig. 12, and (d) Poincaré section of vertical oscillations in Fig. 12

Grahic Jump Location
Fig. 14

Time history of experimental system with the proposed spring mechanism recorded for controlled rotation: (a) angular axis, (b) vertical oscillations, (c) control voltage, and (d) command signal generated to solid-state relay. It is observed at V = 130 Vrms, fctrl = 2.80 Hz.

Grahic Jump Location
Fig. 15

(a) Phase portrait of angular axis in Fig. 14, (b) amplitude spectra of vertical oscillations in Fig. 14, (c) phase portrait of vertical oscillations in Fig. 14, and (d) Poincaré section of vertical oscillations in Fig. 14

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Fig. 16

Comparison of time histories of accumulated net energy derived using the modified experimental rig for different experimental observations. The AC supply voltage is 130 Vrms.

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