The existence of a solution and a numerical method for the Timoshenko nonlinear wave system
ESAIM: Mathematical Modelling and Numerical Analysis (2010)
- Volume: 38, Issue: 1, page 1-26
- ISSN: 0764-583X
Access Full Article
top
Abstract
topHow to cite
topPeradze, Jemal. "The existence of a solution and a numerical method for the Timoshenko nonlinear wave system." ESAIM: Mathematical Modelling and Numerical Analysis 38.1 (2010): 1-26. <http://eudml.org/doc/194206>.
@article{Peradze2010,
abstract = {
The initial boundary value problem for a beam is
considered in the Timoshenko model. Assuming the analyticity
of the initial conditions, it is proved that the problem is
solvable throughout the time interval. After that, a numerical algorithm,
consisting of three steps, is constructed. The solution is
approximated with respect to the spatial and time variables using
the Galerkin method and a Crank–Nicholson type scheme. The system
of equations obtained by discretization is solved
by a version of the Picard iteration method. The accuracy of
the proposed
algorithm is investigated.
},
author = {Peradze, Jemal},
journal = {ESAIM: Mathematical Modelling and Numerical Analysis},
keywords = {Timoshenko nonlinear system; beam;
Galerkin method; Crank–Nicholson scheme;
Picard process.; existence; initial-boundary value problem for a beam; Galerkin method; Crank-Nicholson type scheme; Picard iteration method},
language = {eng},
month = {3},
number = {1},
pages = {1-26},
publisher = {EDP Sciences},
title = {The existence of a solution and a numerical method for the Timoshenko nonlinear wave system},
url = {http://eudml.org/doc/194206},
volume = {38},
year = {2010},
}
TY - JOUR
AU - Peradze, Jemal
TI - The existence of a solution and a numerical method for the Timoshenko nonlinear wave system
JO - ESAIM: Mathematical Modelling and Numerical Analysis
DA - 2010/3//
PB - EDP Sciences
VL - 38
IS - 1
SP - 1
EP - 26
AB -
The initial boundary value problem for a beam is
considered in the Timoshenko model. Assuming the analyticity
of the initial conditions, it is proved that the problem is
solvable throughout the time interval. After that, a numerical algorithm,
consisting of three steps, is constructed. The solution is
approximated with respect to the spatial and time variables using
the Galerkin method and a Crank–Nicholson type scheme. The system
of equations obtained by discretization is solved
by a version of the Picard iteration method. The accuracy of
the proposed
algorithm is investigated.
LA - eng
KW - Timoshenko nonlinear system; beam;
Galerkin method; Crank–Nicholson scheme;
Picard process.; existence; initial-boundary value problem for a beam; Galerkin method; Crank-Nicholson type scheme; Picard iteration method
UR - http://eudml.org/doc/194206
ER -
References
top- S. Bernstein, On a class of functional partial differential equations. AN SSSR, Moscow, Selected Works. Izd. 3 (1961) 323–331.
- M. Hirschhorn and E. Reiss, Dynamic buckling of a nonlinear Timoshenko beam. SIAM J. Appl. Math.34 (1979) 230–301.
- S. Timoshenko, Théorie des vibrations. Béranger, Paris (1947).
- M. Tucsnak, On an initial boundary value problem for the nonlinear Timoshenko beam. Ann. Acad. Bras. Cienc.63 (1991) 115–125.
NotesEmbed ?
topYou must be logged in to post comments.
To embed these notes on your page include the following JavaScript code on your page where you want the notes to appear.