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Nonlinear Dynamics

, Volume 53, Issue 1–2, pp 129–138 | Cite as

Simply supported elastic beams under parametric excitation

  • In-Soo Son
  • Yuusuke Uchiyama
  • Walter Lacarbonara
  • Hiroshi Yabuno
Original Paper

Abstract

In this paper, the nonlinear characteristics of the parametric resonance of simply supported elastic beams are investigated. Considering a geometrically exact formulation for unsharable and inextensible elastic beams subject to support motions, the integral-partial-differential equation of motion is obtained. The third-order perturbation of the equation of motion is then determined in a form amenable to an asymptotic treatment. The method of multiple scales is used to obtain the equations that describe the modulation of the amplitude and phase of parametric-resonance motions. The stability and bifurcations of the system are investigated considering, in particular, the frequency-response function. Furthermore, experimental results are shown to confirm the theoretically predicted stability and bifurcations.

Keywords

Parametric excitation Cosserat theory Nonlinear inertia Nonlinear elastic rod Experimental frequency-response curve Method of multiple scales 

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Copyright information

© Springer Science+Business Media B.V. 2007

Authors and Affiliations

  • In-Soo Son
    • 1
  • Yuusuke Uchiyama
    • 2
  • Walter Lacarbonara
    • 3
  • Hiroshi Yabuno
    • 2
  1. 1.Department of Mechanical EngineeringDong-eui UniversityBusanSouth Korea
  2. 2.Graduate School of Systems and Information EngineeringUniversity of TsukubaTsukubaJapan
  3. 3.Dipartimento di Ingegneria Strutturale e GeotecnicaUniversity of Rome La SapienzaRomeItaly

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