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

Aslanyan A., Dronka J.

Journal of Mathematics and Applications

2007

Vol. 29

53-73

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.