BIFURCATION AND CHAOS OF A THIN RECTANGULAR SIMPLY SUPPORTED PLATE WITH LARGE DEFLECTION IN A COUPLED ENVIRONMENT OF HEATING, FORCE AND MAGNETIC FIELD

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Journal of Vibration and Shock ›› 2013, Vol. 32 ›› Issue (7) : 129-134.

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BIFURCATION AND CHAOS OF A THIN RECTANGULAR SIMPLY SUPPORTED PLATE WITH LARGE DEFLECTION IN A COUPLED ENVIRONMENT OF HEATING, FORCE AND MAGNETIC FIELD

Chen-shumei Wang-ping Wang-zhiren Bai-xiangzhong

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Abstract

In this paper, the chaotic motion for large deflection of a thin plate simply supported on the four sides and unmovable in a coupled environment of mechanical load, magnetic field and temperature field is investigated. Based on the theory of plates and shells and magnetic elasticity and considering the effect of temperature field, the nonlinear magnetic elastic coupled vibration equations of the rectangular plate in the coupled environment of a transverse steady magnetic field and mechanical load is derived. Using Melnikov function method, the chaotic motion condition of the dynamic system under the meaning of Smale horseshoe transformation is obtained.The numerical simulations about the vibration equation of the system are also presented. Through specific example, the bifurcation diagram, the displacement wave diagram, the phase diagram and the Poincare section diagram of this system are shown here. The influences of the parameters variation of mechanical load, magnetic field and temperature field to the chaotic motion of this system are discussed. From the simulation, the vibration characters of this system can be controlled by changing the parameters of mechanical load, magnetic field and temperature field.

Key words

Large deflection / Thermal-magneto elasticity / Coupling field / Melnikov function method / Bifurcation / Chaos

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Chen-shumei Wang-ping Wang-zhiren Bai-xiangzhong. BIFURCATION AND CHAOS OF A THIN RECTANGULAR SIMPLY SUPPORTED PLATE WITH LARGE DEFLECTION IN A COUPLED ENVIRONMENT OF HEATING, FORCE AND MAGNETIC FIELD [J]. Journal of Vibration and Shock, 2013, 32(7): 129-134