Geodesic
Tikhonov well-posedness of the identification problem for fixing conditions for mechanical systems
Sibirskij žurnal industrialʹnoj matematiki, Tome 15 (2012) no. 4, pp. 24-37

Voir la notice de l'article provenant de la source Math-Net.Ru

The problem of the identification of fixing conditions is considered for distributed mechanical systems from three natural frequencies of their oscillations. Basing on the Plücker condition, which appears in the reconstruction of a matrix from its minors of maximal order, we construct the well-posedness set of the problem and prove its Tikhonov well-posedness. For a wide class of problems, we find an explicit solution to the identification problem for the matrix of boundary conditions written down in terms of the characteristic determinant of the corresponding spectral problem. We give examples of the solution of specific problems of mechanics and a counterexample showing that two natural frequencies are not enough for the uniqueness in the identification of the boundary conditions.
Keywords: Tikhonov well-posedness, inverse problem, identification of boundary conditions, distributed mechanical systems, natural frequencies, eigenvalues.
Mots-clés : Plücker condition 
@article{SJIM_2012_15_4_a2,
     author = {A. M. Akhtyamov and A. V. Muftakhov},
     title = {Tikhonov well-posedness of the identification problem for fixing conditions for mechanical systems},
     journal = {Sibirskij \v{z}urnal industrialʹnoj matematiki},
     pages = {24--37},
     publisher = {mathdoc},
     volume = {15},
     number = {4},
     year = {2012},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/SJIM_2012_15_4_a2/}
}
TY  - JOUR
AU  - A. M. Akhtyamov
AU  - A. V. Muftakhov
TI  - Tikhonov well-posedness of the identification problem for fixing conditions for mechanical systems
JO  - Sibirskij žurnal industrialʹnoj matematiki
PY  - 2012
SP  - 24
EP  - 37
VL  - 15
IS  - 4
PB  - mathdoc
UR  - http://geodesic.mathdoc.fr/item/SJIM_2012_15_4_a2/
LA  - ru
ID  - SJIM_2012_15_4_a2
ER  - 
%0 Journal Article
%A A. M. Akhtyamov
%A A. V. Muftakhov
%T Tikhonov well-posedness of the identification problem for fixing conditions for mechanical systems
%J Sibirskij žurnal industrialʹnoj matematiki
%D 2012
%P 24-37
%V 15
%N 4
%I mathdoc
%U http://geodesic.mathdoc.fr/item/SJIM_2012_15_4_a2/
%G ru
%F SJIM_2012_15_4_a2
A. M. Akhtyamov; A. V. Muftakhov. Tikhonov well-posedness of the identification problem for fixing conditions for mechanical systems. Sibirskij žurnal industrialʹnoj matematiki, Tome 15 (2012) no. 4, pp. 24-37. http://geodesic.mathdoc.fr/item/SJIM_2012_15_4_a2/