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Nonlinear Dynamics of High-Dimensional Models of a Rotating Euler-Bernoulli Beam Under the Gravity Load

[+] Author Affiliations
J. L. Huang

Sun Yat-sen University, Guangzhou, China

W. D. Zhu

Harbin Institute of Technology, Harbin, ChinaUniversity of Maryland, Baltimore County, Baltimore, MD

Paper No. IMECE2014-37157, pp. V04BT04A050; 16 pages
doi:10.1115/IMECE2014-37157
From:
  • ASME 2014 International Mechanical Engineering Congress and Exposition
  • Volume 4B: Dynamics, Vibration, and Control
  • Montreal, Quebec, Canada, November 14–20, 2014
  • Conference Sponsors: ASME
  • ISBN: 978-0-7918-4648-3
  • Copyright © 2014 by ASME

abstract

Nonlinear dynamic responses of an Euler-Bernoulli beam attached to a rotating rigid hub with a constant angular velocity under the gravity load are investigated. The slope angle of the centroid line of the beam is used to describe its motion, and the nonlinear integro-partial differential equation that governs the motion of the rotating hub-beam system is derived using Hamilton’s principle. Spatially discretized governing equations are derived using Lagrange’s equations based on discretized expressions of kinetic and potential energies of the system, yielding a set of second-order nonlinear ordinary differential equations with combined parametric and forced harmonic excitations due to the gravity load. The incremental harmonic balance (IHB) method is used to solve for periodic responses of high-dimensional models of the system and period-doubling bifurcation. The multivariable Floquet theory along with the precise Hsu’s method is used to investigate the stability of the periodic responses. Phase portraits and bifurcation points obtained from the IHB method agree very well with those from numerical integration.

Copyright © 2014 by ASME

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