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Research Papers

Nonlinear Dynamics of Inverted Pendulum Driven by Airflow

[+] Author and Article Information
B. R. Nana Nbendjo

Laboratory of Modelling and Simulation in Engineering and Biological Physics,  University of Yaounde I, Box 812, Yaounde, Cameroon; Max-Planck-Institut für Physik Komplexer Systeme, Nöthnitzer Str. 38, D-01187 Dresden, Germanynananbendjo@yahoo.com

J. Comput. Nonlinear Dynam 7(1), 011013 (Oct 24, 2011) (5 pages) doi:10.1115/1.4004963 History: Received October 04, 2010; Revised August 11, 2011; Accepted August 24, 2011; Published October 20, 2011; Online October 24, 2011

A nonlinear model of inverted pendulum that exhibit unbounded single well φ6 potential is described. The complete equation for one-dimensional wind-induced sway is derived. The harmonic balance method along with Melnikov theory are used to seek the effects of aerodynamic drag forces on the amplitude of vibration, on the structure failure, and on the appearance of horseshoes chaos. Numerical simulations have been performed to confirm analytical investigation.

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Figures

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Figure 1

An inverted pendulum

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Figure 2

Phase diagram of an unbounded single well φ6 potential

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Figure 3

Escape boundary in space parameter (Ω,uo)

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Figure 4

Appearance of horseshoes chaos in space parameter (Ω,uo)

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Figure 5

Regular shape of the basin for uo=2.5

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Figure 6

Fractals basin boundaries for uo=23

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