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Xuezhang Hou (2003)
International Journal of Applied Mathematics and Computer Science
A dynamic system with structural damping described by partial differential equations is investigated. The system is first converted to an abstract evolution equation in an appropriate Hilbert space, and the spectral and semigroup properties of the system operator are discussed. Finally, the well-posedness and the asymptotical stability of the system are obtained by means of a semigroup of linear operators.
Tunc Geveci, Ian Christie (1989)
ESAIM: Mathematical Modelling and Numerical Analysis - Modélisation Mathématique et Analyse Numérique
Gratus, J., Tucker, R. W. (2003)
Journal of Applied Mathematics
Jemal Peradze (2004)
ESAIM: Mathematical Modelling and Numerical Analysis - Modélisation Mathématique et Analyse Numérique
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...
Jemal Peradze (2010)
ESAIM: Mathematical Modelling and Numerical Analysis
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...
Avalos, George (1996)
Abstract and Applied Analysis
Cezary Graczykowski, Tomasz Lewiński (2005)
Control and Cybernetics
Hedrih, Katica (2006)
Mathematical Problems in Engineering
Jeongho Ahn (2008)
ESAIM: Mathematical Modelling and Numerical Analysis
In this work, we consider dynamic frictionless contact with adhesion between a viscoelastic body of the Kelvin-Voigt type and a stationary rigid obstacle, based on the Signorini's contact conditions. Including the adhesion processes modeled by the bonding field, a new version of energy function is defined. We use the energy function to derive a new form of energy balance which is supported by numerical results. Employing the time-discretization, we establish a numerical formulation and investigate...
Eduard Feireisl (1988)
Aplikace matematiky
The author investigates time-periodic solutions of the quasilinear beam equation with the help of accelerated convergence methods. Using the Newton iteration scheme, the problem is approximated by a sequence of linear equations solved via the Galerkin method. The derivatiove loss inherent to this kind of problems is compensated by taking advantage of smoothing operators.
Franco Pastrone (1992)
Rendiconti del Seminario Matematico della Università di Padova
Medhat Abbassi (1987)
Collectanea Mathematica
Guo, Bao-Zhu, Song, Qian (1995)
Journal of Applied Mathematics and Stochastic Analysis
Ahmed Abbas Mizeal, Mudhir A. Abdul Hussain (2012)
Archivum Mathematicum
In this paper, we are interested in the study of bifurcation solutions of nonlinear wave equation of elastic beams located on elastic foundations with small perturbation by using local method of Lyapunov-Schmidt.We showed that the bifurcation equation corresponding to the elastic beams equation is given by the nonlinear system of two equations. Also, we found the parameters equation of the Discriminant set of the specified problem as well as the bifurcation diagram.
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