Thermoelastic System Research Articles

Coupled Thermoelastic Vibration of the Axially Moving Sandwich Beam

The transverse vibration characteristic of the viscoelastic sandwich beam with axial speed is studied under the coupled temperature field and displacement field. Based on the theory of Euler - Bernouli beam and the constitutive relation of Kelvin viscoelastic material model, the transverse vibration equation of the axially moving beam is established ; considering the interaction of the material deformation and the heat conduction, the coupled governing equation of the beam is obtained. and the coupled thermoelastic dynamics system are obtained by Galerkin method. The related thermal parameters on the vibration frequency are analyzed by using numerical method.

Uniqueness and stability of an inverse kernel problem for type III thermoelasticity

In this paper, we establish a global Carleman estimate for a thermoelastic system of type III. Based on this estimate, we furthermore study an inverse problem of determining a spatially varying thermal kernel function. We derive Hölder stability for the coefficient inverse problem only by displacement measurements over a given subdomain ω along a sufficiently large time interval and temperature measurements at time t0 over whole domain Ω. The uniqueness for such an inverse problem is yielded as a direct result.

Energy decay in a Timoshenko-type system of thermoelasticity of type III with different wave-propagation speeds

In this paper, we consider a one-dimensional linear Timoshenko system of thermoelasticity type III and prove a polynomial stability result for the non-equal wave-propagation speed case.

On the control of n-dimensional thermoelastic system

In this article, we consider n-dimensional thermoelastic system with a nonlinear weak frictional damping. We establish an explicit and general decay rate result, using some properties of the convex functions. Our result is obtained without imposing any restrictive growth assumption on the damping term.

Asymptotic profiles of solutions for the isothermal Falk–Konopka system of shape memory alloys with weak damping

The aim of this paper is to investigate asymptotic behavior of solutions to the Cauchy problem of certain fourth-order semilinear elastic system with weak damping in three space dimension. The system corresponds to the isothermal case of the thermoelastic system representing the martensitic phase transitions on shape memory alloys. We give several asymptotic profiles of solutions. By considering the second-order expansion of solutions, we obtain more precise information about asymptotic behavior of solutions as t →∞ , and observe the contribution of the nonlinear term to solutions. Moreover, we give the third-order expansion formula which enable us to clarify the relation between the fourth- and the second-order derivative term.

Uniqueness and Hölder type stability of continuation for the linear thermoelasticity system with residual stress

By introducing some auxiliary functions, an elasticity system with thermal effects becomes a coupled hyperbolic-parabolic system. Using this reduced system, we obtain a Carleman estimate with two large parameters for the linear thermoelasticity system with residual stress which is the basic tool for showing stability estimates in the lateral Cauchy problem.

Asymptotic behavior of second sound thermoelasticity with internal time-varying delay

In this paper, we consider a thermoelastic system of second sound with internal time-varying delay. Under suitable assumption on the weight of the delay, we prove, using the energy method, that the damping effect through heat conduction given by Cattaneo’s law is still strong enough to uniformly stabilize the system even in the presence of time delay.

Hot bands and hot spots: Some direct solutions of continuous thermoelastic systems with friction

Hot bands and hot spots are thermoelastic phenomena appearing in frictional systems with high energy dissipation like brake systems or clutches. These thermoelastic instabilities are driven by the interaction of friction-induced heat in the sliding plane and thermal expansion of the materials. Systems exposed to thermoelastic instabilities show a characteristic temperature pattern that can lead to local material damage and vibrations like judder or brake torque fluctuations. While hot bands are observable by a cut through the system normal to the direction of sliding, hot spots are described by a cut parallel to the direction of sliding. When an angle parameter is introduced in a model-based description, both types of thermoelastic instabilities can be described by one single model. Such a model is presented that comprises of layers corresponding to different mechanical parts (e.g. pad, disk, homogenized cooling channels). Every layer is described by field equations for thermoelastic behavior and heat conduction. All layers basically include the same set of solutions which can analytically be found by separation of complex variables. These solutions are scaled to satisfy the boundary conditions at the contact areas between the layers. No symmetry conditions are required, but if present, they can simplify the model. The stability of one thermoelastic phenomenon under investigation is determined by evaluating the characteristic equation of the system. The appearance of hot spots or bands, their spatial distribution and movement are discussed in terms of sliding velocity and other system parameters.

Determination of an unknown source for a thermoelastic system with a memory effect

We study an inverse problem of determining a spatially varying source term in a thermoelastic medium with a memory effect. The coupling phenomena between elasticity and heat as well as the memory effect make such an inverse problem very complicated. We firstly prove a pointwise Carleman estimate for a general strongly coupled hyperbolic system, and then obtain a Carleman estimate for the hyperbolic thermoelastic system. Based on this estimate, we finally establish a Hölder stability for the inverse source problem only by making a displacement measurement on a given subdomain for sufficiently large times, provided the source be known near the boundary. The uniqueness for such an inverse problem is yielded as a direct result.

Optimal rates of decay in 2-d thermoelasticity with second sound

We consider a linear thermoelastic plate system where the heat flux is given by Cattaneo's model. We show that the resulting system is exponentially stable if and only if the rotational inertia coefficient μ is positive. On the other hand, for μ = 0, we establish polynomial stability results giving optimal rates of decay for initial data in the domain of the infinitesimal generator of the thermoelastic semigroup.

Wave propagation and transient heat transfer in thermoelastic composites

We revisit the pioneering works by Ene [1] and Francfort [2] which give the macroscopic equivalent model for wave propagations and transient heat transfers in thermoelastic composite media, by using the method of asymptotic expansions. The obtained model (denoted as model I in the following) shows a similar structure to the classical thermoelastic system which couples the inertial wave equation with the transient heat equation. By analyzing the dimensionless description at the heterogeneity scale and by estimating the dimensionless numbers herein, we show that two very different characteristic frequencies are present. At the higher one, the obtained model (model II) describes wave propagation with memory effects whereas macroscopic transient heat transfers are absent. At the lower frequency, model III describes transient heat transfers while the composite material undergoes a quasi-static deformation. Model III is similar to model I where the inertial term is neglected. Model II is not reducible to model I.

Global existence, asymptotic stability, and uniform attractors for non-autonomous thermoelastic systems with constant time delay

In this paper, we first consider a non-autonomous thermoelastic system with a boundary delay and obtain the asymptotic behavior, then using the contractive function method and multiplier techniques, we establish the asymptotic behavior and the existence of a uniform attractor of the system with a boundary time delay. The main advantage of this method is that we only need to verify compactness condition with the type of energy estimates same as those for establishing the absorbing set. Moreover, we investigate an alternative result of solutions to semilinear thermoelastic systems by virtue of the semigroup method.

Exponential decay in thermoelastic materials with voids and dissipative boundary without thermal dissipation

We study the energy decay of the solutions of a linear homogeneous anisotropic porous thermoelastic system in the context of Green and Naghdi model of type II with the following boundary condition with memory for the displacement \({{\bf T}(x,t)n(x) = -\gamma_0v(x,t) - \int_0^\infty \lambda(s)v^t(x,s) {{d}}s}\) . By introducing a boundary free energy, we prove that if the kernel λ exponentially decays in time, then also the energy exponentially decays when porosity viscosity is present.

Stability and global attractors for thermoelastic Bresse system

The Editor and Publishers Taylor & Francis are retracting the above article from publication in Applicable Analysis. This paper was previously published in online only form as part of Taylor & Fran...

Boundary stabilization of memory-type thermoelasticity with second sound

In this paper, we consider an n-dimensional thermoelastic system of second sound with a viscoelastic damping localized on a part of the boundary. We establish an explicit and general decay rate result that allows a wider class of relaxation functions and generalizes previous results existing in the literature.

Carleman estimate with second large parameter for second order hyperbolic operators in a Riemannian manifold and applications in thermoelasticity cases

In this article we prove a Carleman estimate with second large parameter for a second order hyperbolic operator in a Riemannian manifold ℳ. Our Carleman estimate holds in the whole cylindrical domain ℳ × (0, T) independent of the level set generated by a weight function if functions under consideration vanish on boundary ∂(ℳ × (0, T)). The proof is direct by using calculus of tensor fields in a Riemannian manifold. Then, thanks to the dependency of the second larger parameter, we prove Carleman estimates also for (i) a coupled parabolic-hyperbolic system (ii) a thermoelastic plate system (iii) a thermoelasticity system with residual stress.

Fast Relaxation Solvers for Hyperbolic-Elliptic Phase Transition Problems

Phase transition problems in compressible media can be modelled by mixed hyperbolic-elliptic systems of conservation laws. Within this approach phase boundaries are understood as shock waves that satisfy additional constraints, sometimes called kinetic relations. For numerical approximation tracking-type algorithms have been suggested. The core piece of these algorithms is the usage of exact Riemann solvers incorporating the kinetic relation. However, exact Riemann solvers are computationally expensive or even not available. In this paper we present a class of approximate Riemann solvers for hyperbolic-elliptic models that relies on a generalized relaxation procedure. It preserves in particular the kinetic relation for phase boundaries exactly and gives for isolated phase transitions the correct solutions. In combination with a novel subiteration procedure the approximate Riemann solvers are used in the tracking algorithms. The efficiency of the approach is validated on a barotropic system with linear kinetic relation where exact Riemann solvers are available. For a nonlinear kinetic relation and a thermoelastic system we use the new method to gain information on the Riemann problem. To our knowledge an exact solution for arbitrary Riemann data is currently not available in these cases.

The Global Attractor of Thermoelastic Coupled System

In this paper, we consider a class of Sine-Gordon equations which arise from the model of the thermoelastic coupled rod. Firstly, by virtue of the classical semigroup theory, we prove the existence and uniqueness of the mild solution under certain initial-boundary value for above-mentioned equations. Secondly, we obtain the boundedness of solutions by the priori estimates. Lastly, we prove the existence of a global attractor.

On a higher order two dimensional thermoelastic system combining a local and nonlocal boundary conditions

On a higher order two dimensional thermoelastic system combining a local and nonlocal boundary conditions

On a nonlinear generalized thermoelastic system with obstacle

On a nonlinear generalized thermoelastic system with obstacle