The Discretization Methods of a Rotating Flexible Cantilever Beam

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The dynamics of a rotating flexible cantilever beam is investigated by using assumed mode method, finite element method and Bezier curve interpolation method in this paper. The longitudinal deformation and the transverse deformation of the flexible beam are considered and the coupling term of the deformation which is caused by transverse deformation is included in the expression of longitudinal deformation. The assumed mode, finite element and Bezier interpolation are used to discretize the deformation of the flexible beam, and then the dynamics equations are built by Lagrange equation, and a software package for the dynamic simulation of the rotating cantilever beam is developed. Two cases are considered in the simulations. One is the dynamics study which the external rotating torque is known, another one is that a rotating fixed axis flexible beam falls with gravity. According to the simulation results, assumed mode, finite element and Bezier interpolation method can be well used for discretizing the deformation of the flexible beam; the computational efficiency of finite element method is the lowest, and Bezier interpolation method is the highest; the calculation accuracy of the assumed mode method is lower than the Bezier interpolation method.

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Periodical:

Edited by:

Chunliang Zhang and Paul P. Lin

Pages:

697-707

Citation:

J. H. Fan and D. G. Zhang, "The Discretization Methods of a Rotating Flexible Cantilever Beam", Applied Mechanics and Materials, Vols. 226-228, pp. 697-707, 2012

Online since:

November 2012

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$38.00

[1] R.E. Valembois, P. Fisette and J.C. Samin. Comparison of various techniques for modeling flexible beams in multibody dynamics. Nonlinear Dynamics, Vol. 12 (1997), p.367.

DOI: https://doi.org/10.1023/a:1008204330035

[2] G.P. Cai and J.Z. Hong. Assumed mode method of a rotating flexible beam[J]. Acta Mechanica Sinica, Vol. 1 (2005), p.48 (In Chinese).

[3] G. Xu, G.Z. Wang and W.Y. Chen. Geometric construction of energy-minimizing Bezier curves. Science China, Vol. 54 (2011), pp.1395-1406.

[4] G.G. Sanborn and A.A. Shabana. On the integration of computer aided design and analysis using the finite element absolute nodal coordinate formulation. Multibody Syst Dyn, Vol. 22 (2009), p.181.

DOI: https://doi.org/10.1007/s11044-009-9157-3

[5] G.G. Sanborn and A.A. Shabana. A rational finite element method based on the absolute nodal coordinate formulation. Nonlinear Dyn. Vol. 58 (2009), p.565.

DOI: https://doi.org/10.1007/s11071-009-9501-4

[6] P. Lan and A.A. Shabana. Rational Finite Elements and Flexible Body Dynamics. Journal of Vibration and Acoustics. Vol. 132 (2010), pp.041007-1.

DOI: https://doi.org/10.1115/1.4000970

[7] P. Lan and A.A. Shabana. Integration of B-spline geometry and ANCF finite element analysis. Nolinear Dyn. Vol. 61 (2010), p.193.

DOI: https://doi.org/10.1007/s11071-009-9641-6

[8] G.P. Cai, J.Z. Hong and S.X. Yang. Dynamics analysis of a flexible hub-beam system with tip mass[J]. Mechanics Research Communications. Vol. 32 (2005), p.173.

DOI: https://doi.org/10.1016/j.mechrescom.2004.02.007