Abstract
The complex vibrations and bifurcations of plates modeled as systemswith infinite degrees-of-freedom are considered. Both theBubnov–Galerkin with high-order approximations and finite differencemethods with approximation O(h 4)are applied. In addition, the calculation ofthe Lyapunov exponents of the system is performed, and the results arecompared to those derived by Bennetin's method. Some examples of newnonlinear phenomena exhibited by the considered systems are reported.
This is a preview of subscription content, log in via an institution to check access.
Similar content being viewed by others
References
Awrejcewicz, J., Andrianov, I. V., and Manevitch, L. I., Asymptotic Approach in Nonlinear Dynamics: New Trends and Applications, Springer, Berlin, 1998.
Awrejcewicz, J. and Krysko, V. A., 'Feigenbaum scenario exhibited by thin plate dynamics', Nonlinear Dynamics 24, 2001, 373–398.
Awrejcewicz, J., Mrozowski, J., and Potier-Ferry, M., 'Non-linear behaviour of a rectangular plate exposed to airflow', in Bifurcation and Chaos-Theory and Applications, J. Awrejcewicz (ed.), Springer, Berlin, 1995, pp. 253–272.
Bajaj, A. K. and Johnson, J. M., 'Asymptotic techniques and complex dynamics in weakly nonlinear forced mechanical systems', International Journal of Mechanics 25, 1990, 211–226.
Abe, A., Kobayashi, Y., and Yamada, G., 'Two-mode response of simply supported, rectangular laminated plates', International Journal of Non-Linear Mechanics 33(4), 1998, 675–690.
Nayfeh, T. A. and Vakakis, A. F., 'Subharmonic traveling waves in a geometrically non-linear circular plate', International Journal of Non-Linear Mechanics 29(2), 1994, 233–245.
Wei-Zhang, Zhaomiao, L., and Pei, Y., 'Global dynamics of a parametrically and externally excited thin plate', Nonlinear Dynamics 24, 2001, 245–268.
Lasiecka I., 'Finite dimensionality and compactness of attractors for von Kármán equations with nonlinear dissipation', Nonlinear Differential Equations and Applications 6, 1999, 437–472.
Krysko, V. A., Awrejcewicz, J., and Bruk, V., 'On the solution of a coupled thermo-mechanical problem for non-homogeneous Timoshenko-type shells', Journal of Mathematical Analysis and Applications 273(2), 2002, 409–416.
Krysko, V. A., Awrejcewicz, J., and Bruk, V., 'On existence and uniqueness of solution to coupled thermomechanics problem of non-homogenous isotropic plates', Journal of Applied Analysis 8(1), 2002, 129–139.
Awrejcewicz, J. and Krysko, V. A., Nonclassic Thermoelastic Problems in Nonlinear Dynamics of Shells, Springer, Berlin, 2002.
Awrejcewicz, J., Krysko, V. A., and Krysko, A. V., 'Spatial temporal chaos and solitons exhibited by von Kármán model', International Journal of Bifurcation and Chaos 12(7), 2002, 1465–1513.
Volmir, A. S., Nonlinear Dynamics of Plates and Shells, Nauka, Moscow, 1972 [in Russian].
Fedosev, V. I., 'On the problem of stability of deformable bodies', Applied Mathematics and Mechanics 27(2), 1963, 971–976 [in Russian].
Oseledec, V. I., 'A multiplicative ergodic theorem: Liapunov characteristic numbers for dynamical systems', Transactions of the Moscow Mathematical Society 19, 1968, 197–231.
Bennetin, G., Casartelli, M., Galgani, L., Giorgilli, A., and Strelcyn, J. M., 'On the reliability of numerical study of stochasticity, I: Existence of time averages', Il Nuovo Cimento 44B(1), 1978, 183–195.
Bennetin, G., Casartelli, M., Galgani, L., Giorgilli A., and Strelcyn, J. M., 'On the reliability of numerical studies of stochasticity, II: Identification of time averages', Il Nuovo Cimento 50B, 1979, 211–232.
Pesin, Yu. B., 'Characteristic Lyapunov exponents and smooth ergodic theory', Russian Mathematical Survey 32, 1977, 55–114.
Bul, B., Sinai, A. G., and Chaikin, K.M., 'Feigenbaum universality and thermodynamic formalism', Uspekhi Mathematicheskich Nauk 39(3), 1984, 3–37 [in Russian].
Arneodo, A. and Thual, O., 'Direct numerical simulation of triple convection problem versus normal form prediction', Physics Letters A 109(8), 1985, 367–373.
Arneodo, A., Collet, P. M., Spiegel, E. A., and Tresser, C., 'Asymptotic chaos', Physica D 14(3), 1985, 327–347.
Author information
Authors and Affiliations
Rights and permissions
About this article
Cite this article
Awrejcewicz, J., Krysko, V.A. & Narkaitis, G.G. Bifurcations of a Thin Plate-Strip Excited Transversally and Axially. Nonlinear Dynamics 32, 187–209 (2003). https://doi.org/10.1023/A:1024458814785
Issue Date:
DOI: https://doi.org/10.1023/A:1024458814785