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 differential quadrature method (DQM). The coupled nonlinear partial differential equations for the two-dimensional nonplanar nonlinear vibrations are discretized in space and time domains using DQ 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 use of the Poincare map, the three-dimensional 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.
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Ravindra B, Zhu WD (1998) Low dimensional chaotic response of axially accelerating continuum in the supercritical regime. Arch Appl Mech 68:195–205
Marynowski K (2004) Non-linear vibrations of an axially moving viscoelastic web with time-dependent tension. Chaos Solit Fract 21:481–490
Chen LQ, Yang XD (2006) Transverse nonlinear dynamics of axially accelerating viscoelastic beams based on 4-term Galerkin truncation. Chaos Solit Fract 27(3):748–757
Chen LH, Zhang W, Yang FH (2010) Nonlinear dynamics of higher-dimensional system for an axially accelerating viscoelastic beam with in-plane and out-of-plane vibrations. J Sound Vib 329:5321–5345
Ding H, Chen L (2009) On two transverse nonlinear models of axially moving beams. Sci China Ser E: Technol Sci 52(3):743–751
Ding H, Chen L (2009) Nonlinear dynamics of axially accelerating viscoelastic beams based on differential quadrature. Acta Mech Solida Sin 22(3):267–275
Bellman R, Kashef BG, Casti J (1972) Differential quadrature: a technique for the rapid solution of nonlinear partial differential equations. J Comput Phys 10:40–52
Shu C (2000) Differential quadrature and its application in engineering. Springer, Berlin
Acknowledgment
The authors gratefully acknowledge the support of the National Natural Science Foundation of China (NNSFC) through grant Nos. 11290152, 11072008, 10732020 and 11272016.
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© 2014 The Society for Experimental Mechanics, Inc.
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Wang, D., Zhang, W., Yao, M., Hu, W. (2014). Two-Dimensional Nonlinear Dynamics of Axially Accelerating Beam Based on DQM. In: Kerschen, G. (eds) Nonlinear Dynamics, Volume 2. Conference Proceedings of the Society for Experimental Mechanics Series. Springer, Cham. https://doi.org/10.1007/978-3-319-04522-1_22
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DOI: https://doi.org/10.1007/978-3-319-04522-1_22
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Publisher Name: Springer, Cham
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Online ISBN: 978-3-319-04522-1
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