Chaotic Analysis of Rectangular Thin Plate Based on Fourth-order Runge-Kutta Method

Author(s): 
Y. Zhao, G. W. Zhang, & B. Lin*

Affiliation(s): 

School of Mechanical Engineering, Tianjin University, Tianjin 300072, China
 
Cite this paper
Y. Zhao, G. W. Zhang, B. Lin, “Chaotic Analysis of Rectangular Thin Plate Based on Fourth-order Runge-Kutta Method”, Journal of Mechanical Engineering Research and Developments, vol. 39, no. 3, pp. 625-632, 2016. DOI: 10.7508/jmerd.2016.03.003

ABSTRACT: In practical applications, rectangular thin plate plays a significant role, especially in the case of a variety of magnetic interaction; therefore, its safety is of great importance to concern. This paper studies the nonlinear magneto-elastic vibration and chaotic analysis of clamped rectangular thin plate under different circumstances (including force, magnetic coupling and thermal, force, and magnetic coupling two cases). Firstly, a magnetoelasticity vibration equations of force and magneto-elastic coupling magnetic field is established, with the application of chaotic theory to study it, with fourth-order Runge-Kutta method for simulation analysis, and system Lyapunov exponents diagram and Poincare sectional view are drawn; and then the impact of changes in temperature field on the system is considered, also the equation is established for simulation analysis to identify the influence of parameters on motion characteristics, and then summed up the law, which will play a guiding role for practical applications.

Keywords : Rectangular thin plate; Magnetoelasticity; Chaotic analysis.

References
[1] Y. Zhong, R. Li, and B. Tian, “Hamiltonian analytical solution of clamped rectangular thin plate free vibration”, Chinese Journal of Applied Mechanics, vol. 28, no. 4, pp. 323-327, April 2011.
[2] Y. Y. Gao, G. Tang, and W. Wan, “Dynamics of thin rectangular plate on nonlinear elastic foundation”, Journal of Vibration and Shock, vol. 32, no. 16, pp. 182-186, August 2013.
[3] W. M. Wu, A. Sánchez, and M. Zhang, “An implicit 2-D shallow water flow model on unstructured quadtree rectangular mesh”, Journal of Coastal Research, vol. 59, pp. 15-26, 2015.
[4] G. Ge, H. L. Wang, and J. Xu, “Stochastic bifurcation of thin rectangular plate subjected to in-plane stochastic parametrical excitation”, Journal of Vibration and Shock, vol. 30, no. 9, pp. 253-258, September 2011.
[5] X. S. Cheng and X. L. Du, “The thermal bend of concrete rectangular thin plate with trilateral clamped and one side free”, Engineering Mechanics, vol. 30, no. 4, pp. 97-106, April 2013.
[6] F. Yan, C. Zhang, L. Sun, and D. Zhang, “Experimental study on slamming pressure and hydroelastic vibration of a flat plate during water entry”, Journal of Coastal Research, vol. 73, pp. 594-599, 2015.
[7] X. S. Cheng, X. L. Du, and G. W. Zhang, “The thermal bend of concrete rectangular thin plate with three simply supported and one side free”, Chinese Journal of Applied Mechanics, vol. 30, no. 1, pp. 37-42, January 2013.
[8] F. Tan and Y. L. Zhang, “Thermal bending analysis of simply supported thin plate by the hybrid boundary node method”, Chinese Journal of Solid Mechanics, vol. 33, no. 6, pp. 617-622, June 2012.
[9] D. L. Li, J. Q. Wu, W. X. Peng, W. F. Xiao, J. G. Wu, J. Y. Zhuo, T. Q. Yuan, and R. C. Sun, “Effect of lignin on bamboo biomass self-bonding during hot-pressing: lignin structure and characterization”, BioResources, vol. 10.4, pp. 6769-6782, 2015.
[10] W. Zhang, Y. C. He, and D. X. Cao, “Experimental investigation on nonlinear vibrations of simply supported rectangular thin plate subjected to transverse excitation”, Science & Technology Review, vol. 27, no. 2, pp. 21-24, February 2009.
[11] N. N. Zhu, Z. X. Zhang, and X. L. Liang, “Positive operator of earth theme based on fourth-order runge-kutta method”, Journal of Henan University of Urban Construction, vol. 22, no. 4, pp. 52-55, April 2013.
[12] J. Qin, “Application of runge-kutta method in solving differential equation model”, Anhui: Anhui University, 2010.
[13] R. Kaysar and H. Nurmamat, “Two stage fourth-order runge-kutta method for solving diffusion equation”, Journal of Hubei University (Natural Science Edition), vol. 36, no. 5, pp. 476-480, May 2014.