Hypernormal Form at Cubic of a Rectangular Symmetric Cross-Ply Laminated Composite Plate

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Based on wings flutter on flying aircraft in this paper, the authors study the mechanical model of the rectangular symmetric cross-ply composite laminated plates. Frist, the method of multiple scales is employed to obtain the four-dimensional averaged equations of the model. Then, the method of new grading function and multiple Lie brackets is utilized to obtain the hypernormal form (simplest normal form, unique normal form) at cubic of above averaged equations.

Info:

Periodical:

Advanced Materials Research (Volumes 581-582)

Edited by:

Jimmy (C.M.) Kao, Wen-Pei Sung and Ran Chen

Pages:

641-644

Citation:

W. Y. Jia et al., "Hypernormal Form at Cubic of a Rectangular Symmetric Cross-Ply Laminated Composite Plate", Advanced Materials Research, Vols. 581-582, pp. 641-644, 2012

Online since:

October 2012

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$38.00

[1] Baider, J.A. Sanders, Further Reduction of the Takens-Bogdanov Normal Form, J. Differential Equations. 99 (1992) 205-244.

DOI: https://doi.org/10.1016/0022-0396(92)90022-f

[2] H. Kokubu, H. Oka, D. Wang, Linear Grading Function and Further Reduction of Normal Forms, J. Differential Equations. 132 (1996) 293-318.

DOI: https://doi.org/10.1006/jdeq.1996.0181

[3] D. Wang, J. Li, M.H. Huang, Y. Jiang, Unique Normal Form of Bogdanov-Takens Singularities, J. Differential Equations. 163 (2000) 223-238.

DOI: https://doi.org/10.1006/jdeq.1999.3739

[4] J. Li, D. Wang, W. Zhang, General Forms of the Simplest Normal Form of Bogdanov-Takens Singularities, Dynamics of Continuous, Discrete and Impulsive Systems, Series A: Mathematical Analysis. 8 (2001) 519-530.

[5] J.P. Peng, D. Wang, A Sufficient Condition for the Uniqueness of Normal Forms and Unique Normal Forms of Generalized Hopf Singularities, Inter. J. Bifurcation and Chaos. 14 (2004) 3337-3345.

DOI: https://doi.org/10.1142/s0218127404011247

[6] Y.A. Kuznetsov, Practical Computation of Normal Forms on Center Manifolds at Degenerate Bogdanov-Takens Bifurcations, Inter. J. Bifurcation and Chaos. 15 (2005) 3535-3546.

DOI: https://doi.org/10.1142/s0218127405014209

[7] W. Zhang, H.Y. Hu, New Progress of Nonlinear Dynamics Theory and Application, Science Press, (2009).

[8] B. Gao, W.N. Zhang, Parametric Normal Forms of Vector Fields and Their Further Simplification, Nonlinearity. 23 (2010) 2539–2557.

DOI: https://doi.org/10.1088/0951-7715/23/10/011