We conduct an analysis of a one-dimensional linear problem that describes the vibrations of a connected suspension bridge. In this model, the single-span roadbed is represented as a thermoelastic Shear beam without ro...
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We conduct an analysis of a one-dimensional linear problem that describes the vibrations of a connected suspension bridge. In this model, the single-span roadbed is represented as a thermoelastic Shear beam without rotary inertia. We incorporate thermal dissipation into the transverse displacement equation, following Green and Naghdi's theory. Our work demonstrates the existence of a global solution by employing classical Faedo-Galerkin approximations and three a priori estimates. Furthermore, we establish exponential stability through the application of the energy method. For numerical study, we propose a spatial discretization using finite elements and a temporal discretization through an implicit Euler scheme. In doing so, we prove discrete stability properties and a priori error estimates for the discrete problem. To provide a practical dimension to our theoretical findings, we present a set of numerical simulations.
This paper presents a one-dimensional Bresse system with thermoelasticity of type iii and constant delay. The objective is to investigate and establish the asymptotic behavior of vibrations in a circular arch problem ...
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This paper presents a one-dimensional Bresse system with thermoelasticity of type iii and constant delay. The objective is to investigate and establish the asymptotic behavior of vibrations in a circular arch problem coupled with damping due to the thermal effect subject to constant delay feedback. By applying the semigroup method, we prove that the system is well-posed. Furthermore, with some assumptions on the delay feedback and wave speeds of propagation, we prove that the dissipation through this thermal effect is solely sufficient to counteract the time delay effect and the vibrations in the displacements, thus causing exponential and polynomial energy decay of the system's solution. Our stability results are achieved by employing the multiplier technique, which mainly involves constructing an appropriate Lyapunov functional equivalent to the system's energy.
In this paper, we investigate a one-dimensional thermoelastic Bresse system, where the heat conduction is given by Green and Naghdi theories. Under some assumptions on the memory kernel and a new introduced stability ...
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In this paper, we investigate a one-dimensional thermoelastic Bresse system, where the heat conduction is given by Green and Naghdi theories. Under some assumptions on the memory kernel and a new introduced stability number, we prove that the unique damping given by the memory term is sufficiently strong to stabilize the system exponentially. In fact, we establish a general decay result from which the exponential and polynomial decays are only special cases.
The convergence result for the thermoelasticity of type iii defined on a semi-infinite cylindrical region is studied. We prove the convergence result for the thermal conductivity b. (C) 2012 Elsevier Ltd. All rights r...
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The convergence result for the thermoelasticity of type iii defined on a semi-infinite cylindrical region is studied. We prove the convergence result for the thermal conductivity b. (C) 2012 Elsevier Ltd. All rights reserved.
In the present paper we consider the linear theory of thermoelasticity of type iii as developed by Green and Naghdi (1992, 1995). Within the context of the harmonic vibrations, we establish some estimates describing t...
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In the present paper we consider the linear theory of thermoelasticity of type iii as developed by Green and Naghdi (1992, 1995). Within the context of the harmonic vibrations, we establish some estimates describing the spatial behavior of the corresponding amplitudes, provided the frequency is lower than a certain critical value. It is shown that such critical frequency is influenced only by the mechanical effects. Extension of results to the strongly elliptic thermoelastic materials is also discussed. (C) 2011 Elsevier Ltd. All rights reserved.
In this paper we consider a thermoelastic system of type distributed delay. Under suitable assumption on the weight of iii with boundary the delay, we prove, using the energy method, that the damping effect through he...
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In this paper we consider a thermoelastic system of type distributed delay. Under suitable assumption on the weight of iii with boundary the delay, we prove, using the energy method, that the damping effect through heat conduction given by Green and Naghdi's theory is still strong enough to uniformly stabilize the system even in the presence of time delay. (C) 2014 Elsevier Inc. All rights reserved.
In this paper, we investigate a one-dimensional porous elastic system of memory-type coupled with thermal effects, knowing that the heat flux used was introduced by Green and Naghdi. We establish a general decay resul...
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In this paper, we investigate a one-dimensional porous elastic system of memory-type coupled with thermal effects, knowing that the heat flux used was introduced by Green and Naghdi. We establish a general decay result irrespective of any condition among the coefficients of the system.
This paper concerns the stability of thermoelastic laminated beams with structural memory, where the heat conduction is given by Green and Naghdi. We establish a general decay result for the system, where exponential ...
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We investigate in this paper a thermoelastic system where the oscillations are defined by the Timoshenko model and the heat conduction is given by Green and Naghdi theories. We introduce 2 new stability numbers (1) , ...
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We investigate in this paper a thermoelastic system where the oscillations are defined by the Timoshenko model and the heat conduction is given by Green and Naghdi theories. We introduce 2 new stability numbers (1) , (2), and we prove a general decay result, from which the exponential and polynomial decays are only special cases.
This paper deals with the model proposed for nonsimple materials with heat conduction of typeiii. We analyze first the general system of equations, determine the behavior of its solutions with respect to the time, an...
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This paper deals with the model proposed for nonsimple materials with heat conduction of typeiii. We analyze first the general system of equations, determine the behavior of its solutions with respect to the time, and show that the semigroup associated with the system is not analytic. Two limiting cases of the model are studied later. Copyright (c) 2015John Wiley & Sons, Ltd.
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