Hypernormal Form at Cubic of Honeycomb Sandwich Plate Dynamics Model

Abstract:

Honeycomb sandwich plate have been widly applied in industry design in recent years. In this paper, we study the cubic hypernormal form (the simplest normal form and the unique normal form) for honeycomb sandwich plate dynamics model with the help of Maple symbolic computation. Firstly, we get the average equation of four dimensional cartesian form by using the method of multiple scales perturbation analysis. Based on the method combined new grading function with multiple Lie brackets, we obtain the hypernormal form of cubic truncated. The results will further enrich the research for dynamics of honeycomb sandwich plate model, and is also the basis for higher order normal form research.

• Periodical: Applied Mechanics and Materials (Volume 437)
• Pages: 81-84
• DOI: https://doi.org/10.4028/www.scientific.net/AMM.437.81
• Online since: October 2013
• Authors: Xin Li, Jing Li*, Bin He
• Keywords: Honeycomb Sandwich Plate, Hypernormal Form, Method of Multiple Scales, New Grading Function

References

[1] J. van der Geer, J.A.J. Hanraads, R.A. Lupton, The art of writing a scientific article, J. Sci. Commun. 163 (2000) 51-59.

[1] Othman A. R, Barton D. C, Failure initiation and propagation characteristics of honeycomb sandwich composites, J. Sci. Composite Structures. 36 (2008) 126-138.

DOI: 10.1016/j.compstruct.2007.10.034

[2] Burlayenko V. N, Sadowski T, Effective elastic properties of foam-filled honeycomb cores of sandwich panels, J. Sci. Composite structures. 92 (2010) 2890-2900.

DOI: 10.1016/j.compstruct.2010.04.015

[3] A. Baider , J. Sanders, Further reduction of the Bogdanov-Takens normal form, J. Sci. Journal of Differential Equations. 99 (1992) 205-244.

DOI: 10.1016/0022-0396(92)90022-f

[4] S. Ushiki, Normal forms for singularities of vector fields, J. Sci. Japan Journal of Industrial and Applied Mathematics. 1 (1984) 1-37.

DOI: 10.1007/bf03167860

[5] Duo. Wang, An introduction to the normal form theory of ordinary diferential equations, J. Sci. Advances In Mathematics. 19 (1990) 38-71.

[6] Duo Wang, Jing Li, Minhai Huang, Young Jiang, Unique Normal Form of Bogdanov-Takens Singularities, J. Sci. Journal of Differential Equations. 163 (2000) 223-238.

DOI: 10.1006/jdeq.1999.3739

[7] Hiroshi Kokubu, Hiroe Oka, Duo Wang, Linear Grading Function and Further Reduction of Normal Forms, J. Sci. Journal of Differential Equations. 132 (1996) 293-318.

DOI: 10.1006/jdeq.1996.0181

[8] Jianping Peng, Duo Wang, A sufficient condition for the uniqueness of normal forms and unique normal forms of generalized Hopf singularities, J. Sci. International Journal of Bifurcation and Chaos. 14 (2004) 3337-3345.

DOI: 10.1142/s0218127404011247

[9] Xiao chen Mao, Hai yan Hu. Stability and Hopf bifurcation of a delayed network of four neurons with a short-cut connection[J]. International Journal of Bifurcation and Chaos. 2008, 18, (10): 3053-3072.

DOI: 10.1142/s021812740802224x

[10] Wei Zhang, Meijuan Gao, Minghui Yao, Zhigang Yao, Higher-dimensional chaotic dynamics of a composite laminated piezoelectric rectangular plate, J. Sci. Science in China Series G Physics Mechanics and Astronomy. 8 (2009).

DOI: 10.1007/s11433-009-0225-8

[2] W. Strunk Jr., E.B. White, The Elements of Style, third ed., Macmillan, New York, 1979. Reference to a chapter in an edited book.

[3] G.R. Mettam, L.B. Adams, How to prepare an electronic version of your article, in: B.S. Jones, R.Z. Smith (Eds. ), Introduction to the Electronic Age, E-Publishing Inc., New York, 1999, pp.281-304.

[4] R.J. Ong, J.T. Dawley and P.G. Clem: submitted to Journal of Materials Research (2003).

[5] P.G. Clem, M. Rodriguez, J.A. Voigt and C.S. Ashley, U.S. Patent 6, 231, 666. (2001).

[6] Information on http: /www. weld. labs. gov. cn.