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Abstract: We studied the problem of bifurcation and chaos in a 4-side fixed rectangular thin plate in electromagnetic and mechanical fields. Based on the basic nonlinear electro-magneto-elastic motion equations for a rectangular thin plate and the expressions of electromagnetic forces, the vibration equations are derived for the mechanical loading in a steady transverse magnetic field. Using the melnikov function method, the criteria are obtained for chaos motion to exist as demonstrated by the Smale horseshoe mapping. The vibration equations are solved numerically by a fourth-order runge-Kutta method. Its bifurcation diagram, Lyapunov exponent diagram, displacement wave diagram, phase diagram and Poincare section diagram are obtained.

[1] Awrejcewicz, J., Krysko, V.A., Narkaitis, G.G., 2003. Bifurcations of a thin plate-strip excited transversally and axially. Nonlinear Dynamics, 32(2):187-209.

[2] Awrejcewicz, J., Krysko, V.A., Krysko, A.V., 2004. Complex parametric vibrations of flexible rectangular plates. Mechanicals, 39(3):221-244.

[3] Awrejcewicz, J., Krysko, V.A., Narkaitis, G.G., 2006. Nonlinear vibration and characteristics of flexible plate-strips with non-symmetric boundary conditions. Communications in Nonlinear Science and Numerical Simulation, 11(1):95-124.

[4] Bai, X.Z., 1996a. Magnetoelasticity, thermal-magneto-elasticity and their applications. Advances in Mechanicals, 26(3):389-406 (in Chinese).

[5] Bai, X.Z., 1996b. Basic Elastic-magnetic Theory of Plate and Shell. Machinery Industry Publishing House, Beijing (in Chinese).

[6] Chang, W.P., Wang, S.M., 1986. Thermo-mechanicalally coupled nonlinear vibration of plates. International Journal of Non-Linear Mechanics, 21(5):375-389.

[7] Chen, Y.S., 1993. Bifurcation and Chaos Theory of Nonlinear Oscillation System. Higher Education Publishing House, Beijing (in Chinese).

[8] Huang, R.S., 2000. Chaos and Application. Wuhan University Publishing Company, Wuhan (in Chinese).

[9] Nowacki, W., 1975. Dynamic Problems of Thermo-elasticity. Sijthoff and Noordhoff International Publishers, Leyden, p.123-262.

[10] Pan, E., 2001. Exact solution for simply supported and multilayered magneto-electro-elastic plate. ASME Journal of Applied Mechanicals, 68:608-618.

[11] Pan, E., Heyliger, P.R., 2002. Free vibrations of simply supported and multilayered magneto-electro-elastic plates. Journal of Sound and Vibration, 252(3):429-442.

[12] Pan, E., Han, F., 2005. Exact solution for functionally graded and layered magneto-electro-elastic plates. International Journal of Engineering Science, 43(3-4):321-339.

[13] Trajkorski, D., Cukic, R., 1999. A coupled problem of thermo-elastic vibrations of a circular plate with exact boundary conditions. Mechanics Research Communications, 26(2):217-224.

[14] Wang, J.G., Chen, L.F., Fang, S.S., 2003. State vector approach to analysis of multilayered magneto-electro-elastic plates. International Journal of Solids and Structures, 40(7):1669-1680.

[15] Xu, Z.L., 1988. Elasticity. Higher Education Publishing House, Beijing (in Chinese).

[16] Zhang, W., Liu, Z.M, Yu, P., 2001. Global dynamics of a parametrically and externally excited thin plate. Nonlinear Dynamics, 24(3):245-268.