Journal ArticleDOI
Stabilization of the Timoshenko Beam by Thermal Effect
TLDR
In this paper, the authors considered a linear system of Timoshenko type in a bounded interval and showed that damping occurs through a thermal effect by coupling the system with a heat equation suggested by Green and Naghdi.Abstract:
We consider a linear system of Timoshenko type in a bounded interval No dissipative mechanism is added in the system or at the edges of the beam The damping occurs through a thermal effect by coupling the system with a heat equation suggested by Green and Naghdi We prove exponential decay of solutions of the augmented systemread more
Citations
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Existence and general stabilization of the Timoshenko system of thermo-viscoelasticity of type III with frictional damping and delay terms
TL;DR: In this paper, the authors considered the Timoshenko system of type III with frictional damping and delay terms and proved the global existence of solutions by using the Faedo-Galerkin approximations together with some energy estimates.
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Stabilization of a viscoelastic Timoshenko beam
TL;DR: In this article, an exponential decay of solutions for a large class of kernels with weaker conditions than the existing ones in the literature is proved, which will allow the use of other types of viscoelastic material for Timoshenko type beams than the usually used ones.
Journal ArticleDOI
Exponential decay for a viscoelastically damped timoshenko beam
TL;DR: In this article, it was shown that for a non-decreasing function (Gamma) whose "logarithmic derivative" is decreasing to zero, the decay is exponential.
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A contact problem for a thermoelastic Timoshenko beam
TL;DR: In this article, a dynamic contact problem between a Timoshenko beam and two rigid obstacles is considered and the global existence in time of solutions is found by considering related penalized problems, proving some a priori estimates and passing to the limit.
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Viscoelastic Timoshenko Beams with Occasionally Constant Relaxation Functions
TL;DR: In this paper, it was shown that if we wish to have a decay of order γ(t), then the kernels should be of the same order as the relaxation function, i.e., their product with this function should be summable.
References
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Journal ArticleDOI
Thermoelasticity without energy dissipation
Albert Edward Green,P. M. Naghdi +1 more
TL;DR: In this article, a general uniqueness theorem for linear thermoelasticity without energy dissipation is proved and a constitutive equation for an entropy flux vector is determined by the same potential function which also determines the stress.
Journal ArticleDOI
On undamped heat waves in an elastic solid
Albert Edward Green,P. M. Naghdi +1 more
TL;DR: In this article, the authors focused on the thermal properties of the constitutive response functions in the context of both nonlinear and linear theories, and provided an easy comparison of the one-dimensional version of the equation for the determination of temperature in the linearized theory.
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A Re-Examination of the Basic Postulates of Thermomechanics
Albert Edward Green,P. M. Naghdi +1 more
TL;DR: In this paper, the basic postulates of the purely mechanical theory for a continuum (including its specialization for a rigid body) are re-examined in the context of flow of heat in a rigid solid with particular reference to the propagation of thermal waves at finite speed.
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Boundary control of the Timoshenko beam
Jong Uhn Kim,Yuriko Renardy +1 more
TL;DR: In this paper, it is shown that the Timoshenko beam can be uniformly stabilized by means of a boundary control, and a numerical study on the spectrum is also presented, showing that the beam is uniformly stabilized with respect to the boundary control.
Journal ArticleDOI
Energy decay for Timoshenko systems of memory type
TL;DR: The exponential decay is proved for exponential kernels, while polynomial kernels are shown to lead to a polyn coefficients decay, and the optimality of the results is investigated.