Geometrically nonlinear free transversal vibrations of thin-walled elongated panels with arbitrary generatrix

• Autorzy: Marchuk M. , Goriachko T. , Pakosh V.
• Konferencja: Symposium “Vibrations In Physical Systems” (26 ; 04-08.05.2014 ; Będlewo koło Poznania ; Polska)
• Języki publikacji: EN

Abstrakty

EN

The algorithm for finding a finite number of the first values of natural frequencies and forms of geometrically nonlinear free transverse vibrations of thin-walled elongated panels with arbitrary generatrix is proposed and verified. Under normal coordinate quadratic the approximation of displacements is used. Along the tangential coordinates used one-dimensional finite elements. The discrete variation problem is built. For its solving the perturbation method is applied. The numerical results are compared with previously obtained by other authors.

Słowa kluczowe

EN

elongated panels; vibrations; nonlinearity; perturbation method

PL

panele podłużne; drgania; nieliniowość; metoda perturbacji

• Wydawca: Poznan University of Technology. Institute of Applied Mechanics
• Czasopismo: Vibrations in Physical Systems
• Rocznik: 2014
• Tom: Vol. 26
• Strony: 153--160
• Opis fizyczny: Bibliogr. 11 poz., rys., wykr.

Twórcy

autor

Marchuk M.

• 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 T.

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

autor

Pakosh V.

• 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: Cambridge Univ. Press, 2008.
• 2. M. Amabili, Nonlinear vibrations of rectangular plates with different boundary conditions: theory and experiments, Comput. Struct., 82(2004) 2587 – 2605.
• 3. G. Korn, T. Korn, Handbook of high society mathematics, M.: Nauka, 1974.
• 4. V. D. Kubenko, P. S. Kovalchuk, N. P. Podchasov, Nonlinear vibrations of cylindrical shells, K.: Vyshcha Shkola, 1989.
• 5. L. V. Kurpa, N. A. Budnikov, Investigation of forced nonlinear vibrations of laminated shallow shells using a multimode approximation, Bulletin of Donetsk Univ. Serіes A. Natural Sciences, 1(2013) 55 – 60.
• 6. R. Lewandowski, Analysis of strongly nonlinear free vibration of beams using perturbation method, Civil and Env. Eng. Reports, 1(2005) 153–168.
• 7. M. Marchuk, I. Mukha, T. Goriachko, A comparative analysis of the characteristics of geometrically nonlinear stress-strain state of composite plates and cylindrical panels on the basis refied model and elasticity theory, Modelling and Stability: Abstracts of Conference Reports, K: Taras Shevchenko National Univ. of Kyiv, 2011.
• 8. M. Marchuk, V. Pakosh, O. Lesyk, I. Hurayewska, Influence of Pliability to Transversal Deformations of Shear and Compression on Correlation Frequency from Amplitude for Nonlinear Oscillations of Composite Plates, Vibrations in Physical Systems, 22(2006) 251–256.
• 9. N. F. Morozov, Selected two-dimensional problem of elasticity theory, Leningrad: Publishing House of Leningrad. University Press, 1978.
• 10. J. N. Reddy, An introduction to nonlinear finite element analysis, Oxford Univ. Press, 2004.
• 11. A. S. Volmir, Nonlinear dynamics of plates and shells, M.: Nauka, 1972.