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Nonlinear Dynamics of a Loosely Supported Beam Subject to Harmonic Excitation

[+] Author Affiliations
Jakob Knudsen

Malmö University, Malmö, Sweden

Ali R. Massih

Quantum Technologies AB, Uppsala, Sweden

Paper No. IMECE2002-32518, pp. 1305-1312; 8 pages
doi:10.1115/IMECE2002-32518
From:
  • ASME 2002 International Mechanical Engineering Congress and Exposition
  • 5th International Symposium on Fluid Structure Interaction, Aeroelasticity, and Flow Induced Vibration and Noise
  • New Orleans, Louisiana, USA, November 17–22, 2002
  • Conference Sponsors: Applied Mechanics Division
  • ISBN: 0-7918-3659-2 | eISBN: 0-7918-1691-5, 0-7918-1692-3, 0-7918-1693-1
  • Copyright © 2002 by ASME

abstract

The nonlinear dynamic behavior of damped beam oscillator with elastic two-sided amplitude constraints is analyzed. The structure is modeled by a Bernoulli-Euler beam supported by elastic springs. Finite element method is used for discretization in space and time integration is performed by Newmark’s method. Rayleigh damping is assumed for the structure. Symmetric and elastic double-impact motions, both harmonic and subharmonic, are studied by way of a Poincaré mapping that relates the states at subsequent impacts. We have found that by increasing the forcing frequency (ω) for the beam at a certain frequency a stable period one motion (solution) turns into a stable period two motion and subsequently without bifurcation it transits to an infinite number of solutions characteristic of chaotic behavior. By further increasing ω a series of windows in the bifurcation diagram (impact velocity vs. ω) comprising periodic solutions within the chaotic domain appear.

Copyright © 2002 by ASME

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