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

Y. Zhao, G. W. Zhang, & B. Lin*


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.

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