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Zhurnal Vychislitel'noi Matematiki i Matematicheskoi Fiziki, 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
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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.
Received: 01.11.2004
Revised: 05.03.2005
Bibliographic databases:
Document Type: Article
UDC: 519.624.2
Language: Russian
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://mathscinet.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
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    		Журнал вычислительной математики и математической физики Computational Mathematics and Mathematical Physics
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