Pavel Drábek, Herbert Leinfelder, Gabriela Tajčová (1999)
Applications of Mathematics
We consider nonlinearly coupled string-beam equations modelling time-periodic oscillations in suspension bridges. We prove the existence of a unique solution under suitable assumptions on certain parameters of the bridge.
Ioan Ionescu, Quoc-Lan Nguyen (2002)
International Journal of Applied Mathematics and Computer Science
The dynamic evolution with frictional contact of a viscoelastic body is considered. The assumptions on the functions used in modelling the contact are broad enough to include both the normal compliance and the Tresca models. The friction law uses a friction coefficient which is a non-monotone function of the slip. The existence and uniqueness of the solution are proved in the general three-dimensional case.
Oanh Chau, Viorica Motreanu (2002)
International Journal of Applied Mathematics and Computer Science
We consider dynamic problems which describe frictional contact between a body and a foundation. The constitutive law is viscoelastic or elastic and the frictional contact is modelled by a general subdifferential condition on the velocity, including the normal damped responses. We derive weak formulations for the models and prove existence and uniqueness results. The proofs are based on the theory of second-order evolution variational inequalities. We show that the solutions of the viscoelastic problems...
Kuttler, Kenneth, Shillor, Meir (2004)
Electronic Journal of Differential Equations (EJDE) [electronic only]
Kuttler, Kenneth L. (2007)
Electronic Journal of Differential Equations (EJDE) [electronic only]
Jong Yeoul Park, Sun Hye Park (2006)
Czechoslovak Mathematical Journal
We consider the damped semilinear viscoelastic wave equation with nonlocal boundary dissipation. The existence of global solutions is proved by means of the Faedo-Galerkin method and the uniform decay rate of the energy is obtained by following the perturbed energy method provided that the kernel of the memory decays exponentially.
Hassan Ibrahim (2009)
Annales de l'I.H.P. Analyse non linéaire
Giacomo Caviglia, Angelo Morro (2002)
Rendiconti del Seminario Matematico della Università di Padova
Janusz Mika (1971)
Studia Mathematica
Arezki Touzaline (2010)
Annales Polonici Mathematici
The paper deals with the problem of quasistatic frictionless contact between an elastic body and a foundation. The elasticity operator is assumed to vanish for zero strain, to be Lipschitz continuous and strictly monotone with respect to the strain as well as Lebesgue measurable on the domain occupied by the body. The contact is modelled by normal compliance in such a way that the penetration is limited and restricted to unilateral contraints. In this problem we take into account adhesion which...
Joseph, Kayyunnapara Thomas (2005)
Electronic Journal of Differential Equations (EJDE) [electronic only]
Chudinovich, Igor, Constanda, Christian (2003)
Georgian Mathematical Journal
Josef Malík (2004)
Applications of Mathematics
A model of a cable stayed bridge is proposed. This model describes the behaviour of the center span, the part between pylons, hung on one row of cable stays. The existence, the uniqueness of a solution of a time independent problem and the continuous dependence on data are proved. The existence and the uniqueness of a solution of a linearized dynamic problem are proved. A homogenizing procedure making it possible to replace cables by a continuous system is proposed. A nonlinear dynamic problem connected...
Sideris, Thomas C. (2000)
Annals of Mathematics. Second Series
Mikael Barboteu, Jose Ramon Fernández, Youssef Ouafik (2008)
ESAIM: Mathematical Modelling and Numerical Analysis
In this work, we consider the quasistatic frictionless contact problem between a viscoelastic piezoelectric body and a deformable obstacle. The linear electro-viscoelastic constitutive law is employed to model the piezoelectric material and the normal compliance condition is used to model the contact. The variational formulation is derived in a form of a coupled system for the displacement and electric potential fields. An existence and uniqueness result is recalled. Then, a fully discrete scheme...
Maria I. M. Copetti (2004)
ESAIM: Mathematical Modelling and Numerical Analysis - Modélisation Mathématique et Analyse Numérique
In this paper we consider a hyperbolic-parabolic problem that models the longitudinal deformations of a thermoviscoelastic rod supported unilaterally by an elastic obstacle. The existence and uniqueness of a strong solution is shown. A finite element approximation is proposed and its convergence is proved. Numerical experiments are reported.
Maria I.M. Copetti (2010)
ESAIM: Mathematical Modelling and Numerical Analysis
In this paper we consider a hyperbolic-parabolic problem that models the longitudinal deformations of a thermoviscoelastic rod supported unilaterally by an elastic obstacle. The existence and uniqueness of a strong solution is shown. A finite element approximation is proposed and its convergence is proved. Numerical experiments are reported.
Nguyen Thanh Long, Pham Ngoc Dinh, Alain, Tran Ngoc Diem (2005)
Boundary Value Problems [electronic only]
Oanh Chau (2006)
Applications of Mathematics
In this paper, we are interested in the dynamic evolution of an elastic body, acted by resistance forces depending also on the displacements. We put the mechanical problem into an abstract functional framework, involving a second order nonlinear evolution equation with initial conditions. After specifying convenient hypotheses on the data, we prove an existence and uniqueness result. The proof is based on Faedo-Galerkin method.
Barboteu, M., Hoarau-Mantel, T.-V., Sofonea, M. (2003)
Journal of Applied Mathematics