Thermoelastic damping in strain gradient microplates according to a generalized theory of thermoelasticity

Borjalilou, Vahid; Asghari, Mohsen

doi:10.1080/01495739.2020.1722771

Cited by 50 publications

(10 citation statements)

References 60 publications

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“…In this case, a specific temperature field and quite specific deformations for the second phase, which are determined by relations ( 22) and ( 16), (18)(19) are realized for the equilibrium structure. Note that, if the coupled parameters tend to zero, then the problems of thermoelasticity and stationary thermal conductivity are completely separated, and their solutions correspond to the gradient equilibrium case or the classical representation if the gradient parameters are equal to zero.…”

Section: Resultsmentioning

confidence: 99%

“…It should be noted that the one-dimensional analogue of the Eshelby problem [31][32][33], implemented for coupled gradient thermoelasticity, also leads to the algebraic Equation (22), in which the transition matrix connects the stress-strain state of a homogeneous deformation at infinity with the stress state of a composite two-phase rod. Condition (22) allows us to reduce formally the problem of constructing a contact problem to an algebraic problem using the general representation (18), (19) for the temperature and displacement potentials:…”

Section: Transition Matrixmentioning

confidence: 99%

“…To ensure the uniqueness of the solution, it is also necessary to eliminate the displacement of the inhomogeneous structure as a solid as a whole, since the contact conditions (20) determine displacements up to a constant. As a result, we can obtain the following two additional relations for the coefficients from representations (18), (19) for the one-dimensional Eshelby problem:…”

Section: Transition Matrixmentioning

confidence: 99%

“…In recent work [18], a coupled gradient thermoelasticity model and a dual-phase-lag heat conduction model were used to study the processes of thermoelastic damping in strain gradient microplates. Simular model is applied in [19] to study the thermal heat problem of a homogeneous and isotropic long cylinder due to initial stress and heat source.…”

Section: Introductionmentioning

confidence: 99%

“…As a rule, the effects of coupling are limited by taking into account the coupling of temperature fields with volumetric deformation and the corresponding dynamic effects determined by the generalized laws of heat conduction [16][17][18][19][20][21], etc. In this connection, the novelty of the present work lies in the fact that it attempts to take into account the effects of higher order coupling between the gradients of the temperature fields and the gradients of the deformation fields.…”

Section: Introductionmentioning

confidence: 99%

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Analytical Solution of Stationary Coupled Thermoelasticity Problem for Inhomogeneous Structures

2021

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A mathematical statement for the coupled stationary thermoelasticity is given on the basis of a variational approach and the contact boundary problem is formulated to consider inhomogeneous materials. The structure of general representation of the solution from the set of the auxiliary potentials is established. The potentials are analyzed depending on the parameters of the model, taking into account the restrictions associated with additional requirements for the positive definiteness of the potential energy density for the coupled problem in the one-dimensional case. The novelty of this work lies in the fact that it attempts to take into account the effects of higher order coupling between the gradients of the temperature fields and the gradients of the deformation fields. From a mathematical point of view, this leads to a change in the roots of the characteristic equation and affects the structure of the solution. Contact boundary value problems are formulated for modeling inhomogeneous materials and a solution for a layered structure is constructed. The analysis of the influence of the model parameters on the structure of the solution is given. The features of the distribution of mechanical and thermal fields in the region of phase contact with a change in the parameters, which are characteristic only for gradient theories of coupled thermoelasticity and stationary thermal conductivity, are discussed. It is shown, for example, that taking into account the additional parameter of connectivity of gradient fields of deformations and temperatures predicts the appearance of rapidly changing temperature fields and significant localization of heat fluxes in the vicinity of phase contact in inhomogeneous materials.

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Section: Resultsmentioning

confidence: 99%