Vibrations of a weakly nondegenerate 1D-3D multi-structure

• Autorzy: Aslanyan A. G. , Dronka J. , Mishuris G. , Selsil O.
• Języki publikacji: EN

Abstrakty

EN

We study the effect of the transition between degenerate and nondegenerate configurations for a 1D-3D multi-structure, by considering a particular nondegenerate configuration. Analytical asymptotic formulae are derived for the first six eigenfrequencies which include information about the location of the 1D parts (legs) of the multi-structure. This enables us to analyse the transition region by moving the legs closer to each other. Accuracy of the asymptotic formulae is compared with numerical solution for the pile structure (skeleton) and with finite element computations. Some inaccuracies associated with numerical and finite element computations are discussed. In addition, a discussion on two-sided estimates for the eigenfrequencies is also included.

Słowa kluczowe

EN

1D-3D multi structure; finite element analysis; eigenfrequency; vibrations; degeneracy of multi structure

PL

1D-3D multi structura; metoda elementów skończonych; częstotliwość drgań własnych; drgania; degeneracja multi struktur

• Wydawca: Instytut Podstawowych Problemów Techniki PAN
• Czasopismo: Archives of Mechanics
• Rocznik: 2006
• Tom: Vol. 58, nr 1
• Strony: 17--43
• Opis fizyczny: Bibliogr. 12 poz.

Twórcy

autor

Aslanyan A. G.

autor

Dronka J.

autor

Mishuris G.

autor

Selsil O.

• Druzhba, St. 5, kv. 355, Khimki, Moscow Region 141400, Russia

Bibliografia

• 1. V.G. Maz'ya, S.A. Nazarov, B.A. Plamenevskii, Asymptotische Theorze elliptischer Randwertaufgaben in singular gestorten Gebieten, Akademie-Verlag Berlin, B.I, 1991; B.2, 1992.
• 2. P.G. Ciarlet, Mathematical elasticity, Vol. II: Theory of plates, North-Holland, Amsterdam 1997.
• 3. V.A. Kozlov, V.G. Maz'ya, A.B. Movchan, Asymptotic analysis of fields in multi-structures, Oxford University Press, 1999.
• 4. V.A. Kozlov, V.G. Maz'ya, A.B. Movchan, Asymptotic analysis of a mixed boundary value problem in a multi-structure, Asymptotic Analysis, 8, 105-143, 1994.
• 5. V.A. Kozlov, V.G. Maz'ya, A.B. Movchan, Asymptotic representation of elastic fields in a multi-structure, Asymptotic Analysis, 11, 343-415, 1995.
• 6. V.A. Kozlov, V.G. Maz'ya, A.B. Movchan, Fields in nondegenerate 3D-1D elastic multi-structures, LiTH-MAT-R-96-14, Preprint, Linkoping University, 1996.
• 7. A.G. Aslanyan, A.B. Movchan, 0. Selsil, Vibrations of multi-structures including elastic shells: Asymptotic analysis, Euro. J. of Applied Mathematics, 11, 109-128, 2002.
• 8. A.G. Aslanyan, A.B. Movchan, 0. Selsil, Estimates for the low eigen frequencies of a multi-structure including an elastic shell, Euro. J. of Applied Mathematics, 14, 313-342, 2003.
• 9. A.G. Aslanyan, A.B. Movchan, 0. Selsil, Asymptotics for the first six eigenfrequencies of a 1D-3D multi-structure, Proceedings of IUTAM international symposium on Asymptotics, Singularities and Homogenisation in Problems of Mechanics, Liverpool, UK, 221-228, 2003.
• 10. S.O. Asplund, Structural mechanics: Classical and matrix methods, Prentice Hall, En-glewood Cliffs, NJ 1966.
• 11. Matlab, 6.5 The language of technical computing, 2002.
• 12. COSMOS/M.20, A complete finite element analysis system, Structural Research & Analysis Corp., 1997.