Multiple Stability and Unpredictable Outcomes in the Chaotic Vibrations of Euler Beams

[+] Author and Article Information
T. Y. Ng

Institute of High Performance Computing, National University of Singapore, 89C Science Park Drive, #02-11/12, The Rutherford, Singapore Science Park 1, Singapore 118261

Xu Daolin

School of Mechanical and Production Engineering, Nanyang Technological University, Nanyang Avenue, Singapore 639798

J. Vib. Acoust 124(1), 126-131 (Sep 01, 2001) (6 pages) doi:10.1115/1.1426072 History: Received November 01, 1999; Revised September 01, 2001
Copyright © 2002 by ASME
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The simply-supported buckled beam layout
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Bifurcation branches of four distinct steady-state responses that coexist in a parameter window, 0.01<F<3.5
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Steady-state responses and Poincare maps for two chosen solutions
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Two initially nearby trajectories (A & B) may diverge to two distinct steady states as shown in the 3-D potential well
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Two-dimensional view of energy-displacement relation within potential well
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Basin boundary diagram of the four coexisting steady-state solutions, P1(a) (black), P1(b) (white), P1(c) (light gray) and P1(d) (dark gray), for the parameter F=1.4




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