Vibrations of strongly degenerated 3D-1D multi-structures: Asymptotic analysis

• Autorzy: Aslanyan A. , Dronka J.
• Języki publikacji: EN

Abstrakty

EN

We consider an eigenvalue problem of three-dimensional elasticity for a multi-structure consisting of a finite three-dimensional solid linked with some thin elastic cyliriders. An asyrnptotic method is used to derive the junction conditions and to obtain the skeleton model for the multi-structure. Explicit asymptotic formulae for various types of degeneracy are given.

Słowa kluczowe

EN

elasticity; multi-structure; vibrations; eigenfreguencies; asymptotic analysis

PL

częstotliwość drgań własnych; analiza asymptotyczna

• Wydawca: Oficyna Wydawnicza Politechniki Rzeszowskiej
• Czasopismo: Journal of Mathematics and Applications
• Rocznik: 2007
• Tom: Vol. 29
• Strony: 53--73
• Opis fizyczny: Bibliogr. 7 poz.

Twórcy

autor

Aslanyan A.

autor

Dronka J.

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

Bibliografia

• [1] A. G. Aslanyan, J. Dronka, G. S. Mishuris, Ö. Selsil, Yibrations of weakly nondegenerate 3D-1D multi-structures, Arch. Mech. 58 (2006), 17-43.
• [2] A. G. Aslanyan, A. B. Movchan, Ö. Selsil, Vibrations of multi-structures including elastic shdls: asymptotic analysis, Euro. J. Appl. Math. 13 (2002), 109-128.
• [3] A. G. Aslanyan, A. B. Movchan, Ö. Selsil, Estimates for the Iow eigenfreguencies of a multi-structure including an elastic shell, Euro. J. Appl. Math. 14 (2003), 313-342.
• [4] A. G. Aslanyan, A. B. Movchan, Ö. Selsil, Asymptotics for the first six eigenfreguencies of a 1D-3D multi-structure, Proceedings of IUTAM International Symposium on Asymptotics, Singularities and Homogenisation in Problems of Mechanics, Liverpool, UK (2003), 221-228.
• [5] P. G. Ciarlet, Mathematical elasticity. Vol. II: Theory of plates. North-Holland, Amsterdam, 1997.
• [6] L. C. Evans, Partial Differential Eguations, American Mathematical Society, Providence, RI, 1998.
• [7] V. A. Kozlov, V. G. Maz'ya, A. B. Movchan, Asymptotic Analysis of Fields in Multi-structures, Oxford Mathematical Monographs, Clarendon Press, Oxford, 1999.