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 Zh. Vychisl. Mat. Mat. Fiz., 2005, Volume 45, Number 8, Pages 1399–1406 (Mi zvmmf610)

Approximation of the eigenfrequencies of a triangular grid of bars

E. M. Bogatov

Branch of The Moscow State Institute of Steel and Alloys Starooskol'skii Technological Institute

Abstract: A rectangular plate is approximated by a regular triangular grid of bars. It is shown that the low-frequency spectrum of the plate is close to that of the grid. The difference between the eigenvalues of the continual and discrete problems is estimated in terms of the periodicity cell. The proof of the main result is based on a finite difference analogue of the Laplacian and on certain facts from the theory of differential equations on graphs.

Key words: triangular grid of bars, low-frequency spectrum, eigenoscillations, eigenvalue problem for fourth-order equations on graphs, latticed plate, plate discretization, hexagonal mesh, finite-difference Laplacian.

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English version:
Computational Mathematics and Mathematical Physics, 2005, 45:8, 1350–1357

Bibliographic databases:
UDC: 519.624.2
Revised: 05.03.2005

Citation: E. M. Bogatov, “Approximation of the eigenfrequencies of a triangular grid of bars”, Zh. Vychisl. Mat. Mat. Fiz., 45:8 (2005), 1399–1406; Comput. Math. Math. Phys., 45:8 (2005), 1350–1357

Citation in format AMSBIB
\Bibitem{Bog05} \by E.~M.~Bogatov \paper Approximation of the eigenfrequencies of a triangular grid of bars \jour Zh. Vychisl. Mat. Mat. Fiz. \yr 2005 \vol 45 \issue 8 \pages 1399--1406 \mathnet{http://mi.mathnet.ru/zvmmf610} \mathscinet{http://www.ams.org/mathscinet-getitem?mr=2191852} \zmath{https://zbmath.org/?q=an:1110.74031} \transl \jour Comput. Math. Math. Phys. \yr 2005 \vol 45 \issue 8 \pages 1350--1357