Abstract
In the present chapter, novel results of the study of chaotic vibration of flexible circular axially symmetric shallow shells subjected to sinusoidal transverse load are presented for four different boundary conditions are presented. The study is conducted with the use of the finite difference method (FDM), which differentiates the study from the majority of research conducted with the finite element method (FEM).
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References
Aranda-Iglesias, D., Vadillo, G., Rodriguez-Martinez, J.A.: Oscillatory behaviour of compressible hyperelastic shells subjected to dynamic inflation: a numerical study. Acta Mech. 228(6), 2187–2205 (2017)
Awrejcewicz, J.: Ordinary Differential Equations and Mechanical Systems. Springer, Berlin (2014)
Awrejcewicz, J., Andrianov, I.V.: Plates and Shells in Nature, Mechanics and Biomechanics. WNT, Fundacja Ksiazka Naukowo-Techniczna, Warsaw (2001) (in Polish)
Awrejcewicz, J., Krysko, V.A., Papkova, I.V.: Dynamics and statics of flexible axially-symmetric shallow shells. Math. Probl. Eng. 2006, ID 35672 (2006)
Banks, J., Brooks, J., Davis, G., Stacey, P.: On Devaney’s definition of chaos. Amer. Math. Monthly 99(4), 332–334 (1992)
Chen, C., Yuan, J., Mao, Y.: Post-buckling of size-depend micro-plate considering damage effects. Nonlinear Dyn. 90(2), 1301–1314 (2017)
Devaney, R.L.: An Introduction to Chaotic Dynamical Systems. Addison-Wesley, Reading, MA (1989)
Feigenbaum, M.J.: The universal metric properties of nonlinear transformations. J. Stat. Phys. 21(6), 669–706 (1979)
Gulick, D.: Encounters with Chaos. McGraw-Hill, NewYork (1992)
Kantz, H.: A robust method to estimate the maximum Lyapunov exponent of a time series. Phys. Lett. A 185, 77–87 (1994)
Knudsen, C.: Chaos without periodicity. Am. Math. Mon. 101, 563–565 (1994)
Krysko, A.V., Awrejcewicz, J., Zakharova, A.A., Papkova, I.V., Krysko, V.A., Chaotic vibrations of flexible shallow axially symmetric shells. Nonlinear Dyn. 91(4), 2271–2291 (2018)
Lozi, R.: Can we trust in numerical computations of chaotic solutions of dynamical systems? In: World Scientific Series on Nonlinear Science. Topology and Dynamics of Chaos in Celebration of Robert Gilmore’s 70th Birthday, vol. 84, pp. 63–98 (2013)
Mehditabar, A., Rahimi, G.H., Tarahhomi, M.H.: Thermo-elastic analysis of a functionally graded piezoelectric rotating hollow cylindrical shell subjected to dynamic loads. Mech. Adv. Mater. Struct. 0, 1–12 (2017)
Medina, L., Gilat, R., Krylov, S.: Modeling strategies of electrostatically actuated initially curved bistable micro-plates. Int. J. Sol. Struct. 118–119, 1339–1351 (2017)
Reissner, E.: Stress and small displacements of shallow spherical shells. J. Math. Phys. 25, 279–300 (1946)
Rosenstein, M.T., Collins, J.J., De Luca, C.J.: A practical method for calculating largest Lyapunov exponents from small data sets. Phys. D 65, 117–134 (1993)
Sedov, L.: Similarity and Dimensional Methods in Mechanics. CRC Press, Boca Raton (1993)
Vlasov, V.Z.: General Theory of Shells and Its Application in Engineering. NASA-TT-F-99 (1964)
Vorovich, I.I.: Nonlinear Theory of Shallow Shells. Springer, New York (1998)
Wolf, A., Swift, J.B., Swinney, H.L., Vastano, J.A.: Determining Lyapunov exponents from a time series. Phys. D 16, 285–317 (1985)
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Awrejcewicz, J., Krysko, V.A. (2020). Chaotic Vibrations of Flexible Shallow Axially Symmetric Shells vs. Different Boundary Conditions. In: Elastic and Thermoelastic Problems in Nonlinear Dynamics of Structural Members. Scientific Computation. Springer, Cham. https://doi.org/10.1007/978-3-030-37663-5_14
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DOI: https://doi.org/10.1007/978-3-030-37663-5_14
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