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

• Autorzy: Marchuk Mykhailo , Goriachko Taras , Kindratskyy Bohdan , Pakosh Vira

Identyfikatory

DOI

10.21008/j.0860-6897.2020.3.16

• 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.

Słowa kluczowe

EN

corrugated shell; geometrically nonlinear vibrations; mathematical model; generalized method of perturbations; amplitude-frequency characteristics

PL

powłoka falista; drgania geometrycznie nieliniowe; model matematyczny; uogólniona metoda perturbacji; charakterystyka amplitudowo-częstotliwościowa

• Wydawca: Poznan University of Technology. Institute of Applied Mechanics
• Czasopismo: Vibrations in Physical Systems
• Rocznik: 2020
• Tom: Vol. 31, nr 3
• Strony: art. no. 2020316
• Opis fizyczny: Bibliogr. 18 poz., wykr.

Twórcy

autor

Marchuk Mykhailo

• 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

Goriachko Taras

• Pidstryhach Institute for Applied Problems of Mechanics and Mathematics, NASU, 3 b Naukova Str., L’viv, 79053, Ukraine

autor

Kindratskyy Bohdan

• National University «L’viv Polytechnic», 12 Bandera Str., L’viv, 79013, Ukraine

autor

Pakosh Vira

• Pidstryhach Institute for Applied Problems of Mechanics and Mathematics, NASU, 3 b Naukova Str., L’viv, 79053, Ukraine

Bibliografia

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• 2. K.-J.Bathe, Finite Element Procedures, 2nd Ed., Watertown, MA 2014.
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• 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.
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• 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).