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On chaotic oscillations of a laminated composite cylinder subject to periodic application of temperature. (English) Zbl 0946.74033

Summary: We explore the chaotic behaviour of a laminated composite cylinder subjected to a rapid periodic heat load. The laminated cylinder comprises eight layers of carbon-epoxy material and is supported by end diaphragms. The analysis is performed using the natural-mode finite element method. We obtain an irregular signal and an attractor. Takens method is used to reconstruct the attractor. For the time series, we compute the largest Lyapunov exponents and the correlation dimension. Various tests are performed in order to distinguish chaos from noise. Thus the proof for the existence of chaos is formally given.

MSC:

74H65 Chaotic behavior of solutions to dynamical problems in solid mechanics
74H45 Vibrations in dynamical problems in solid mechanics
74F05 Thermal effects in solid mechanics
74E30 Composite and mixture properties
80A20 Heat and mass transfer, heat flow (MSC2010)
37N15 Dynamical systems in solid mechanics
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[1] Argyris, J., Andreadis, I., Pavlos, G. and Athanasiou, M., On the influence of noise in the correlation dimension of chaotic attractors. Chaos, Fractals and Noise9,; Argyris, J., Andreadis, I., Pavlos, G. and Athanasiou, M., On the influence of noise in the correlation dimension of chaotic attractors. Chaos, Fractals and Noise9, · Zbl 0933.37045
[2] Argyris, J. H., Faust, G. and Haase, M., An Exploration of Chaos; Argyris, J. H., Faust, G. and Haase, M., An Exploration of Chaos · Zbl 0805.58001
[3] Argyris, J. H. and Mlejnek, H. P., Die Methode der Finite Elemente; Argyris, J. H. and Mlejnek, H. P., Die Methode der Finite Elemente · Zbl 0706.73070
[4] Argyris, J. H. and Mlejnek, H. P., Dynamics of Structures; Argyris, J. H. and Mlejnek, H. P., Dynamics of Structures · Zbl 0792.73001
[5] Argyris, J. H., Tenek, L., Nonlinear and chaotic oscillations of composite plates and shells under periodic heat load. Comput. Methods Appl. Mech. Engng., 1991,115,; Argyris, J. H., Tenek, L., Nonlinear and chaotic oscillations of composite plates and shells under periodic heat load. Comput. Methods Appl. Mech. Engng., 1991,115, · Zbl 0851.73027
[6] Argyris, J. H., Tenek, L., An efficient and locking-free flat anisotropic plate and shell triangular element. Comput. Methods Appl. Mech. Engng., 1994,118,; Argyris, J. H., Tenek, L., An efficient and locking-free flat anisotropic plate and shell triangular element. Comput. Methods Appl. Mech. Engng., 1994,118, · Zbl 0851.73052
[7] Argyris, J. H., Tenek, L., High-temperature bending, buckling and postbuckling of laminated composite plates using the natural mode method. Comput. Methods Appl. Mech. Engng., 1994,117,; Argyris, J. H., Tenek, L., High-temperature bending, buckling and postbuckling of laminated composite plates using the natural mode method. Comput. Methods Appl. Mech. Engng., 1994,117, · Zbl 0847.73018
[8] Argyris, J. H., Tenek, L., Linear and geometrically nonlinear bending of isotropic and multilayered composite plates by the natural mode method. Comput. Methods Appl. Mech. Engng., 1994,113,; Argyris, J. H., Tenek, L., Linear and geometrically nonlinear bending of isotropic and multilayered composite plates by the natural mode method. Comput. Methods Appl. Mech. Engng., 1994,113, · Zbl 0848.73058
[9] Argyris, J. H., Tenek, L., Natural mode method: A practicable and novel approach to the global analysis of laminated composite plates and shell. Appl. Mech. Rev., 1996,49,; Argyris, J. H., Tenek, L., Natural mode method: A practicable and novel approach to the global analysis of laminated composite plates and shell. Appl. Mech. Rev., 1996,49,
[10] Argyris, J. H., Tenek, L., Olofsson, L., Nonlinear free vibrations of composite plates. Comput. Methods Appl. Mech. Engng., 1994,115,; Argyris, J. H., Tenek, L., Olofsson, L., Nonlinear free vibrations of composite plates. Comput. Methods Appl. Mech. Engng., 1994,115,
[11] Bountis, T., Karakasidis, L., Papaioannou, G., Pavlos, G., The determinism and noise in surface temperature time series. Ann. Geophysicae, 1993,11,; Bountis, T., Karakasidis, L., Papaioannou, G., Pavlos, G., The determinism and noise in surface temperature time series. Ann. Geophysicae, 1993,11,
[12] Broomhead, D. S., King, G. P., Extracting qualitative dynamics from experimental data. Physica D, 1986,20,; Broomhead, D. S., King, G. P., Extracting qualitative dynamics from experimental data. Physica D, 1986,20, · Zbl 0603.58040
[13] Grassberg, P., Procaccia, I., Measuring the strangeness of a strange attractors. Physica D, 1983,9,; Grassberg, P., Procaccia, I., Measuring the strangeness of a strange attractors. Physica D, 1983,9, · Zbl 0593.58024
[14] Jenkins, G. M. and Watts, D. G., Spectral Analysis and its Applications; Jenkins, G. M. and Watts, D. G., Spectral Analysis and its Applications · Zbl 0167.17504
[15] Osborne, A. R., Provenzale, A., Finite correlation dimension for stochastic systems with power-law spectra. Physica D, 1989,35,; Osborne, A. R., Provenzale, A., Finite correlation dimension for stochastic systems with power-law spectra. Physica D, 1989,35, · Zbl 0671.60030
[16] Provenzale, A., Smith, L. A., Vio, R., Murane, G., Distinguishing between low-dimensional dynamical and randomness in measure time series. Physica D, 1992,58,; Provenzale, A., Smith, L. A., Vio, R., Murane, G., Distinguishing between low-dimensional dynamical and randomness in measure time series. Physica D, 1992,58,
[17] Takens, F., Detecting strange attractors in turbulence. In Dynamical Systems and Turbulence; Takens, F., Detecting strange attractors in turbulence. In Dynamical Systems and Turbulence
[18] Theiller, J., Galdrilkan, B., Longtin, A., Eudank, S. and Dayne-Farmer, J., Using surrogate data to detect nonlinearity in time series. In Nonlinear Modeling and Forecasting. Studies of Complexity; Theiller, J., Galdrilkan, B., Longtin, A., Eudank, S. and Dayne-Farmer, J., Using surrogate data to detect nonlinearity in time series. In Nonlinear Modeling and Forecasting. Studies of Complexity
[19] Tsonis, A. A., Chaos from Theory to Applications; Tsonis, A. A., Chaos from Theory to Applications
[20] Wolf, A., Swift, J. B., Swinney, H. L., Vastano, J., Determining Lyapunov exponents from a time series. Physica D, 1985,16,; Wolf, A., Swift, J. B., Swinney, H. L., Vastano, J., Determining Lyapunov exponents from a time series. Physica D, 1985,16, · Zbl 0585.58037
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