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 a high-dimensional model of the system for which convergence is reached and its period-doubling bifurcations. 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.
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October 2014
Research-Article
Nonlinear Dynamics of a High-Dimensional Model of a Rotating Euler–Bernoulli Beam Under the Gravity Load Available to Purchase
J. L. Huang,
J. L. Huang
Department of Applied Mechanics
and Engineering,
e-mail: [email protected]
and Engineering,
Sun Yat-sen University
,Guangzhou 510275
, China
e-mail: [email protected]
Search for other works by this author on:
W. D. Zhu
W. D. Zhu
1
Division of Dynamics and Control,
School of Astronautics,
School of Astronautics,
Harbin Institute of Technology
,P.O. Box 137
,Harbin 150001
, China
Department of Mechanical Engineering,
e-mail: [email protected]
University of Maryland--Baltimore County
,1000 Hilltop Circle
,Baltimore, MD 21250
e-mail: [email protected]
1Corresponding author.
Search for other works by this author on:
J. L. Huang
Department of Applied Mechanics
and Engineering,
e-mail: [email protected]
and Engineering,
Sun Yat-sen University
,Guangzhou 510275
, China
e-mail: [email protected]
W. D. Zhu
Division of Dynamics and Control,
School of Astronautics,
School of Astronautics,
Harbin Institute of Technology
,P.O. Box 137
,Harbin 150001
, China
Department of Mechanical Engineering,
e-mail: [email protected]
University of Maryland--Baltimore County
,1000 Hilltop Circle
,Baltimore, MD 21250
e-mail: [email protected]
1Corresponding author.
Contributed by the Applied Mechanics Division of ASME for publication in the JOURNAL OF APPLIED MECHANICS. Manuscript received November 20, 2013; final manuscript received July 16, 2014; accepted manuscript posted July 21, 2014; published online August 14, 2014. Assoc. Editor: Alexander F. Vakakis.
J. Appl. Mech. Oct 2014, 81(10): 101007 (20 pages)
Published Online: August 14, 2014
Article history
Received:
November 20, 2013
Revision Received:
July 16, 2014
Accepted:
July 21, 2014
Citation
Huang, J. L., and Zhu, W. D. (August 14, 2014). "Nonlinear Dynamics of a High-Dimensional Model of a Rotating Euler–Bernoulli Beam Under the Gravity Load." ASME. J. Appl. Mech. October 2014; 81(10): 101007. https://doi.org/10.1115/1.4028046
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