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Application of HDQM for the Analysis of Two-Dimensional Nonlinear Dynamics of Axially Accelerating Beam

[+] Author Affiliations
Dong-Mei Wang

Beijing University of Technology, Beijing, ChinaJining University, Qufu, China

Wei Zhang, Qian Wang

Beijing University of Technology, Beijing, China

Mu-Rong Li

Jinqiao Coal Mine of Jinxiang County, Jining, Shandong, China

Paper No. DETC2014-34139, pp. V008T11A026; 6 pages
doi:10.1115/DETC2014-34139
From:
  • ASME 2014 International Design Engineering Technical Conferences and Computers and Information in Engineering Conference
  • Volume 8: 26th Conference on Mechanical Vibration and Noise
  • Buffalo, New York, USA, August 17–20, 2014
  • Conference Sponsors: Design Engineering Division, Computers and Information in Engineering Division
  • ISBN: 978-0-7918-4641-4
  • Copyright © 2014 by ASME

abstract

In this paper, the two-dimensional nonlinear dynamics are investigated for the nonplanar nonlinear vibrations of an axially accelerating moving viscoelastic beam with in-plane and out-of-plane vibrations by the harmonic differential quadrature method (HDQM). The coupled nonlinear partial differential equations for the two-dimensional nonplanar nonlinear vibrations are discretized in space and time domains using HDQM and Runge-Kutta-Fehlberg methods respectively. Based on the numerical solutions, the nonlinear dynamical behaviors such as bifurcations and chaotic motions of the nonlinear system are investigated by using of the phase portrait and the bifurcation diagrams. The bifurcation diagrams for the in-plane and out-of-plane displacements via the mean axial velocity and the amplitude of velocity fluctuation are respectively presented while other parameters are fixed.

Copyright © 2014 by ASME

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