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Mathematical model and method of determination of amplitude-frequency characteristics of corrugated cylindrical shells for geometrically nonlinear vibrations

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Języki publikacji
EN
Abstrakty
EN
On the basis of spatial geometrically nonlinear theory of elasticity by using quadratic approximations for components of the vector of displacements along the normal coordinate to the median surface is developed a new mathematical model of nonlinear dynamics of cylindrical shells with corrugated configuration for median surface. The perturbation method for the solution of systems of nonlinear differential equations for problems of determination of amplitude-frequency characteristics is generalized. In a combination of finite element and generalized perturbations methods, a new methodology for solving problems of free geometrically nonlinear vibrations of shells with complex guide geometry was developed and verified. With its help the influence of geometrical parameters of corrugating at circular coordinate on the main frequency of the elongated cylindrical panel is investigated.
Rocznik
Strony
art. no. 2020316
Opis fizyczny
Bibliogr. 18 poz., wykr.
Twórcy
  • Pidstryhach Institute for Applied Problems of Mechanics and Mathematics, NASU, 3 b Naukova Str., L’viv, 79053, Ukraine
  • National University «L’viv Polytechnic», 12 Bandera Str., L’viv, 79013, Ukraine
  • Pidstryhach Institute for Applied Problems of Mechanics and Mathematics, NASU, 3 b Naukova Str., L’viv, 79053, Ukraine
  • National University «L’viv Polytechnic», 12 Bandera Str., L’viv, 79013, Ukraine
autor
  • Pidstryhach Institute for Applied Problems of Mechanics and Mathematics, NASU, 3 b Naukova Str., L’viv, 79053, Ukraine
Bibliografia
  • 1. M. Amabili, Nonlinear vibrations and stability of shells and plates, Cambridge Univ. Press, Cambridge 2008.
  • 2. K.-J.Bathe, Finite Element Procedures, 2nd Ed., Watertown, MA 2014.
  • 3. I. Dayyani, A. D. Shaw, E. I. Saavedra Flores, M. I. Friswell, The Mechanics of Composite Corrugated Structures: A Review with Applications in Morphing Aircraft, Composite Structures, 133 (2015) 358-380
  • 4. T. G. Ghazijahani, H. Jiao, D. Holloway, Longitudinally stiffened corrugated cylindrical shells under uniform external pressure, Journal of Constructional Steel Research, 110 (2015) 191-199.
  • 5. G.R. Gulgazaryan, L.G. Gulgazaryan, Vibrations of a corrugated orthotropic cylindrical shell with free edges, Int. Appl. Mech., 42, Issue 12 (2006) 1398-1413.
  • 6. Z. He, G. Liu, W. Jiang, Z. Huang, D. Zhang, Nonlinear Dynamic Responses of a Corrugated Shell Structure under Uniform Load, J. of Eng. Mech., 140, Issue 6 (2014)
  • 7. Y.-W. Kim, Vibration Analysis of Longitudinally Corrugated Cylindrical Shells, Transactions of the Korean Soc. for Noise and Vibration Eng., 26 (2016) 851- 856.
  • 8. A. M. Khalifa, Solving the Vibration Problem of Inhomogeneous Orthotropic Cylindrical Shells with Hoop-Corrugated Oval Cross Section, Comptes Rendus Mécanique, 343, No.9 (2015) 482-494
  • 9. L.V. Kurpa, N.A. Budnikov, Investigation of forced nonlinear vibrations of multilayer hollow shells by means of multimode approximation, Bulletin of Donetsk National University. Series A. Natural Sciences, No.1 (2013) 55-60 [in Russian].
  • 10. R. Lewandowski, Analysis of strongly nonlinear free vibration of beams using perturbation method, Civil and Env. Eng. Reports, 1 (2005) 153-168.
  • 11. R. Lewandowski, Free Vibration of Structures with Cubic Non-linearity-remarks on Amplitude Equation and Rayleigh Quotient, Comput. Methods Appl. Mech. Eng., 192(13) (2003) 1681-1709.
  • 12. M. Marchuk, T. Goriachko, V. Pakosh, Geometrically Nonlinear Free Transversal Vibrations of Thin-Walled Elongated Panels with Arbitrary Generatrix, Vibrations in Physical Systems, 26 (2014) 153-160.
  • 13. M. Marchuk, T. Goriachko, V. Pakosh, Natural Frequencies of Layered Elongated Cylindrical Panels for Geometrically Nonlinear Deformation at Discrete Consideration of Components, Vibrations in Physical Systems, 27 (2016) 255-264.
  • 14. N. F. Morozov, Selected two-dimensional problem of elasticity theory, Publishing House of Leningrad. University Press, Leningrad 1978.
  • 15. J. N. Reddy, An introduction to nonlinear finite element analysis, Oxford Univ. Press, 2004.
  • 16. N. P. Semenyuk, I. Yu. Babich, N. B. Zhukova, Natural Vibrations of Corrugated Cylindrical Shells, Int. Appl. Mech., 41, No.5 (2005), 512-519.
  • 17. Werner Soedel, Vibrations of Shells and Plates, 3rd Ed., Rev. and Expanded, Marcel Dekker, Inc., NY 2004.
  • 18. A. S. Vol’mir, Nonlinear dynamics of plates and shells, Nauka, Moscow 1972 [in Russian].
Uwagi
Opracowanie rekordu ze środków MNiSW, umowa Nr 461252 w ramach programu "Społeczna odpowiedzialność nauki" - moduł: Popularyzacja nauki i promocja sportu (2021).
Typ dokumentu
Bibliografia
Identyfikator YADDA
bwmeta1.element.baztech-d5f8de4b-44e2-459b-babe-a5d42a2dd252
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