This paper describes vibration analysis using the finite element method for a small earphone, especially for the diaphragm shape with a low-rigidity. The viscoelastic diaphragm is supported by multiple nonlinear concentrated springs with linear hysteresis damping. The restoring forces of the nonlinear springs have cubic nonlinearity. The finite elements for the nonlinear springs with hysteresis are expressed and are connected to the diaphragm that is modeled by linear solid finite elements in consideration of a complex modulus of elasticity. Further, the discretized equations in physical coordinates are transformed into the nonlinear ordinary coupled equations using normal coordinates corresponding to the linear natural modes. We computed the nonlinear stationary and non-stationary responses due to the internal resonance between modes with large amplitude in the nonlinear springs and elastic modes in the diaphragm. The non-stationary motions are confirmed as the chaos due to the maximum Lyapunov exponents with a positive number. From the time histories of the deformation distribution in the chaotic vibration, we identified nonlinear modal couplings., {"references":["T. Kondo, T. Sasaki, and T. Ayabe, \"Forced vibration analysis of a\nstraight-line beam structure with nonlinear support elements,\" Trans. Jpn.\nSoc. Mech. Eng., vol. 67, no. 656C, pp. 914-921, 2001.","E. Pesheck, N. Boivin, C. Pierre, and S. W. Shaw, \"Non-linear modal\nanalysis of structural systems using multi-mode invariant manifolds,\"\nNonlinear Dyn., no. 25, pp. 183-205, 2001.","T. Yamaguchi, K. Nagai, S. Maruyama, and T. Aburada, \"Finite element\nanalysis for coupled vibrations of an elastic block supported by a\nnonlinear spring,\" Trans. Jpn. Soc. Mech. Eng., vol. 69, no. 688C, pp.\n3167-3174, 2003.","T. Yamaguchi, N. Nakahara, K. Nagai, S. Maruyama, and Y. Fujii,\n\"Frequency response analysis of elastic blocks supported by a nonlinear\nspring using finite element method,\" Trans. Jpn. Soc. Mech. Eng., vol. 70,\nno. 696C, pp. 2219-2227, 2004.","T. Yamaguchi, T. Saito, K. Nagai, S. Maruyama, Y. Kurosawa, and S.\nMatsumura, \"Analysis of damped vibration for a viscoelastic block\nsupported by a nonlinear concentrated spring using FEM,\" J. Syst. Des.\nDyn., vol. 4, no. 1, pp. 154-165, 2011.","E. H. Dowell, \"Flutter of a buckled plate as an example of chaotic motion\nof a deterministic autonomous system,\" J. Sound Vib., vol. 85-3, pp.\n333-344, 1982.","A. H. Nayfeh and R. A. Raouf, \"Nonlinear Forced Response of Infinitely\nLong Circular Cylindrical Shells,\" J. Appl. Mech., vol. 54, pp. 571-577,\n1987.","X. L. Yang and P. R. Sethna, \"Non-linear phenomena in forced vibrations\nof a nearly square plate: Antisymmetric case,\" J. Sound Vib., vol. 155-3,\npp. 413-441, 1992.","A. Wolf, J. B. Swift, H. L. Swinney, and J. A. Vastano, \"Determining\nLyapunov exponents from a time series,\" Physica, vol. 16D, pp. 285-317,\n1985.\n[10] O. C. Zienkiewicz and Y. K. Cheung, The Finite Element Method in\nStructural and Continuum Mechanics. New York: MacGraw-Hill, 1967."]}