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Research Papers

# Dynamics of an Electromechanical System With Angular and Ferroresonant Nonlinearities

[+] Author and Article Information
D. O. Tcheutchoua Fossi

Faculty of Science,Laboratory of Modelling and Simulation in Engineering and Biological Physics, and TWAS Research Unit,  University of Yaounde I, P.O. Box 812, Yaoundé, Cameroon

P. Woafo

Faculty of Science,Laboratory of Modelling and Simulation in Engineering and Biological Physics, and TWAS Research Unit,  University of Yaounde I, P.O. Box 812, Yaoundé, Cameroonpwoafo1@yahoo.fr

J. Vib. Acoust 133(6), 061018 (Nov 28, 2011) (7 pages) doi:10.1115/1.4004938 History: Received April 28, 2009; Revised March 19, 2010; Published November 28, 2011; Online November 28, 2011

## Abstract

The purpose of this paper is to study the dynamics of an electromechanical system consisting of a torsion-bar or two mechanical pumps activated by an electromotor. Oscillatory solutions showing the jump and hysteresis phenomena are obtained using the harmonic balance method and direct numerical simulation. Chaotic behavior is presented via the bifurcation diagrams and corresponding Lyapunov exponent. Some implications of the results on the applications of the devices are discussed.

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## Figures

Figure 1

(a) - Electromechanical-torsion bar system. (b) - Electromotor-mechanical pump system.

Figure 2

Amplitudes of electrical part (a) and mechanical part (b) as a function of the normalized frequency. Curves from the harmonic balance approximation (+) and curves from the direct numerical simulation (o) with the parameters of Table 1 and σ=0.5 E=6.5,i0=0.5A,θ0=0.25rad.

Figure 3

Amplitudes of the electrical part (a) and mechanical part (b) as a function of the normalized frequency with the parameters of Fig. 2 and σ=0.5,E=1.5

Figure 4

Bifurcation diagram (a) and Lyapunov exponent (b) against E, with the parameters of Fig. 2 and σ=2, ω=1.338

Figure 5

Amplitudes of electrical part (a) and mechanical part (b) as a function of the normalized frequency. Curves from the harmonic balance approximation (+) and curves from the direct numerical simulation (o) with the parameters of Fig. 2 and γ=0.5.

Figure 6

Bifurcation diagram (a) and Lyapunov exponent (b) against Eγ, with the parameters of Fig. 3 and γ=1.5, σ=0.5, ω=1.338

Figure 7

Bifurcation diagram (a) and Lyapunov exponent (b) against γ, with the parameters of Fig. 3 and Eγ=15, σ=0.5, ω=1.338

Figure 8

Electromechanical diagrams of x-y (a) and x-dydτ (b) with the parameters of Fig. 6 and Eγ=15

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