Showing papers on "Thermoelastic damping published in 2017"

Effect of thermal loading due to laser pulse on thermoelastic porous medium under G-N theory

Abstract: The aim of this paper is to study the wave propagation of generalized thermoelastic medium with voids under the effect of thermal loading due to laser pulse with energy dissipation. The material is a homogeneous isotropic elastic half-space and heated by a non-Gaussian laser beam with the pulse duration of 0.2 ps. A normal mode method is proposed to analyse the problem and obtain numerical solutions for the displacement components, stresses, temperature distribution and the change in the volume fraction field. The results of the physical quantities have been illustrated graphically by comparison between both types II and III of Green-Naghdi theory for two values of time, as well as with and without void parameters.

The effect of a dipolar structure on the Hölder stability in Green–Naghdi thermoelasticity

Abstract: This study is concerned with the mixed initial boundary value problem for a dipolar body in the context of the thermoelastic theory proposed by Green and Naghdi. For the solutions of this problem we prove a result of Holder’s-type stability on the supply terms. We impose middle restrictions on the thermoelastic coefficients, which are common in continuum mechanics. For the same conditions we propose a continuous dependence result with regard to the initial data.

Analytical solution of thermoelastic interaction in a half-space by pulsed laser heating

Abstract: In this article, we consider the problem of a two-dimensional thermoelastic half-space in the context of generalized thermoelastic theory with one relaxation time. The surface of the half-space is taken to be traction free and thermally insulated. The solution of the considered physical quantity can be broken down in terms of normal modes. The nonhomogeneous basic equations have been written in the form of a vector-matrix differential equation, which is then solved by an eigenvalue approach. The exact analytical solution is adopted for the temperature, the components of displacement and stresses. The results obtained are presented graphically for the effect of laser pulse to display the phenomena physical meaning. The graphical results indicate that the thermal relaxation time has a great effect on the temperature, the components of displacement and the components of stress.

Thermoelastic analysis of functionally graded graphene reinforced rectangular plates based on 3D elasticity

Abstract: Thermoelastic bending behaviour of novel functionally graded polymer nanocomposite rectangular plate reinforced with graphene nanoplatelets (GPLs) whose weight fraction varies continuously and smoothly along the thickness direction is investigated. The generalized Mian and Spencer method is utilized to obtain the analytical solutions of nanocomposite rectangular plate with two opposite edges simply supported and under a uniformly distributed transverse load and a temperature change. Three GPL distribution patterns are considered. Comparison between the present analytical solutions and those available in literature is carried out to verify the accuracy of our analytical solutions. A parametric study is conducted to examine the effects of GPL’s weight fraction, distribution pattern, geometry and size as well as the temperature change and plate boundary conditions on the stress and deformation fields of the nanocomposite plates. Numerical results show that the addition of GPLs at a very low content can have a significant reinforcing effect on the thermo-mechanical response of the plate.

A dislocation density-based continuum model of the anisotropic shock response of single crystal α-cyclotrimethylene trinitramine

Abstract: We have developed a model for the finite deformation thermomechanical response of α-cyclotrimethylene trinitramine (RDX). Our model accounts for nonlinear thermoelastic lattice deformation through a free energy-based equation of state developed by Cawkwell et al. (2016) in combination with temperature and pressure dependent elastic constants, as well as dislocation-mediated plastic slip on a set of slip systems motivated by experimental observation. The kinetics of crystal plasticity are modeled using the Orowan equation relating slip rate to dislocation density and the dislocation velocity developed by Austin and McDowell (2011) , which naturally accounts for transition from thermally activated to dislocation drag limited regimes. Evolution of dislocation density is specified in terms of local ordinary differential equations reflecting dislocation–dislocation interactions. This paper presents details of the theory and parameterization of the model, followed by discussion of simulations of flyer plate impact experiments. Impact conditions explored within this combined simulation and experimental effort span shock pressures ranging from 1 to 3 GPa for four crystallographic orientations and multiple specimen thicknesses. Simulation results generated using this model are shown to be in strong agreement with velocimetry measurements from the corresponding plate impact experiments. Finally, simulation results are used to motivate conclusions about the nature of dislocation-mediated plasticity in RDX.

Thermoelastic nonlinear frequency analysis of CNT reinforced functionally graded sandwich structure

Abstract: The nonlinear eigen frequency response of the functionally graded single-walled carbon nanotube reinforced sandwich structure is investigated numerically considering the Green-Lagrange nonlinear strain under uniform thermal environment. The mathematical model of the sandwich plate has been derived using the simple higher-order shear deformable kinematics including the temperature dependent properties of each constituent. The sandwich panel constitutes of graded carbon nanotube face sheets and homogeneous core. The desired nonlinear finite element solutions are obtained via the direct iterative method. Based on the necessary validation and convergence new results are computed for different design related parameters and discussed subsequently.

Response of a semiconducting infinite medium under two temperature theory with photothermal excitation due to laser pulses

Abstract: A novel model of two-dimensional deformations for two-temperature theory at the free surface under the excitation of thermoelastic wave by pulsed laser for a semi-infinite semiconducting medium is studied. The effect of mechanical force during a photothermal process is investigated. The mathematical methods of the Lord–Shulman (LS includes one relaxation time) and Green–Lindsay (GL with two relaxation times) theories as well as the classical dynamical coupled theory (CD) are used. An exact expression for displacement components, force stresses, carrier density and distribution of temperature are obtained using the harmonic wave analysis. Combinations of two-temperature and photothermal theories are obtained analytically. Comparisons of the results are made between the three theories also. The effects of thermoelectric coupling parameter, two-temperature parameter on the displacement component, force stress, carrier density, and distribution of temperature for silicon (Si) medium have been illustrated graphically. The variations of the considered variables with the horizontal distance have been discussed.

Nonlinear thermoelastic frequency analysis of functionally graded CNT-reinforced single/doubly curved shallow shell panels by FEM

Abstract: In this article, the nonlinear vibration frequencies of functionally graded carbon nanotube-reinforced composite doubly curved shell panels under elevated thermal environment are numerically investigated using finite element method. The doubly curved carbon nanotube-reinforced shell panel has been modeled mathematically using higher-order kinematics theory and Green–Lagrange geometrical nonlinear strains. The properties of the individual constituents of the graded composite are assumed to be temperature dependent. In addition, the properties of the media are obtained based on the modified rule of mixture. The carbon nanotubes are dispersed nonuniformly through the thickness direction. The large deformation kinematic effects on the structural responses are counted by including all the nonlinear higher-order terms in the formulation. The desired nonlinear responses are computed numerically using our in-house computer code in conjunction with the direct iterative scheme. The convergence and the accur...

Two-temperature plane strain problem in a semiconducting medium under photothermal theory

Abstract: In this investigation, we study the two-temperature problem with two-dimensional (2-D) deformations for a semi-infinite semiconducting medium at the free surface with the influence of mechanical force through a photothermal process. The harmonic wave method (Normal Mode analysis) has been used to get the exact expression of normal displacement, normal force stress, carrier density, and temperature distribution, and also the two-temperature coefficients ratios has been obtained analytically. The effects of several parameters as thermoelastic and thermoelectric coupling parameters and two-temperature parameter of this force on the displacement component, force stress, carrier density, and temperature distribution have been depicted graphically.

Effect of microtemperatures for micropolar thermoelastic bodies

Abstract: In this paper we investigate the theory of micropolar thermoelastic bodies whose micro-particles possess microtemperatures. We transform the mixed initial boundary value problem into a temporally evolutionary equation on a Hilbert space and after that we prove the existence and uniqueness of the solution. We also approach the study of the continuous dependence of solution upon initial data and loads.

Generalized magneto-thermoelastic half-space with diffusion under initial stress using three-phase-lag model

Abstract: The present paper is aimed at studying the effect of initial stress and the magnetic field on thermoelastic interactions in an isotropic, thermally and electrically conducting half-space whose surface is subjected to mechanical and thermal loads. The formulation is applied under the thermoelasticity theory with three-phase-lag, proposed by Choudhuri (2007). The normal mode analysis is used to obtain the expressions for the variables considered. Numerical and computations are performed for a specific material and the results obtained are represented graphically. Comparisons are made with the results predicted by different theories Lord–Shulman theory (L–S), the theory of thermoelasticity type III (G-N III) and the three-phase-lag model (3PHL) in the absence and presence of the initial stress and magnetic field.

Analysis of functionally graded nanodisks under thermoelastic loading based on the strain gradient theory

Abstract: In this paper, the thermoelastic behavior of a functionally graded nanodisk is studied based on the strain gradient theory. It is assumed that the nanodisk thickness is constant, and a power-law model is adopted to describe the variation of functionally graded material properties. Furthermore, the nanodisk angular acceleration is taken to be zero while it is subjected to an axisymmetric loading. Also, it is assumed that any variation in temperature occurs only in the radial direction. The equilibrium equation and the boundary conditions are deduced from Hamilton’s principle. The obtained results are compared with those of classical theory. These results show that both theories predict the same trend for the variation in radial displacements. The differences between the stresses obtained from classical and strain gradient theories are clearly highlighted. Increasing the value of the material inhomogeneity parameter, n, considerably affects the magnitudes and the corresponding peak values of the high-order stress $$\bar{\tau }_{rrr}$$ . Any rise in temperature at the outside radius has a direct effect on the total stresses and radial displacements in the nanodisk. Also, the effects of external load at the inner and outer radii on radial displacement as well as stress components are fully investigated.

A novel solution of fractional order heat equation for photothermal waves in a semiconductor medium with a spherical cavity

Abstract: In this paper, we consider a one dimensional problem of waves in a thermoelastic infinite medium with a spherical cavity. We are concerned with the study a new model of fractional order heat conduction law for a spherical cavity of a semiconductor medium. The governing equations are solved under the effect of the theory of coupled plasma, elastic, thermal waves through a photothermal process. The inner surface of the cavity is taken traction free with thermal shock. Time-dependence is removed by Laplace transform technique to governing equations. This method has been used to get the exact expression of some physical quantities, thermal activation coupling parameters and illustrated graphically.

Nonlinear dynamic thermoelastic response of rectangular FGM plates with longitudinal velocity

Abstract: This study investigates nonlinear dynamic thermoelastic response of functionally graded material (FGM) plates with longitudinal velocity for the first time. The large amplitude motion of FGM plates is considered so that the present model includes both geometry and material nonlinearities. Based on the D'Alembert's principle, the out-of-plane equation of motion of the system is obtained by considering the thermal effect and the longitudinal velocity. After that, the Galerkin method is employed to discretize the partial differential equation of motion to a set of ordinary differential equations. The method of harmonic balance is used to solve analytically the time-varying set of ordinary differential equations. The approximately analytical solutions are verified by numerical solutions utilizing an adaptive step-size fourth-order Runge-Kutta technique. Furthermore, the stability of steady-state response is analyzed for the approximately analytical solutions. The linear frequency characteristics and nonlinear frequency-response characteristics are both presented for the system. The nonlinear frequency-response relationships demonstrate strong hardening-type behavior of the system. Results are shown to examine the influences of different parameters including longitudinal velocity, temperature, constituent volume distribution, in-plane pretension, damping and force amplitude on the nonlinear dynamic thermoelastic response of FGM plates with longitudinal velocity.

Combining the AFLOW GIBBS and elastic libraries to efficiently and robustly screen thermomechanical properties of solids

Abstract: Thorough characterization of the thermomechanical properties of materials requires difficult and time-consuming experiments. This severely limits the availability of data and is one of the main obstacles for the development of effective accelerated materials design strategies. The rapid screening of new potential materials requires highly integrated, sophisticated, and robust computational approaches. We tackled the challenge by developing an automated, integrated workflow with robust error-correction within the AFLOW framework which combines the newly developed ``Automatic Elasticity Library'' with the previously implemented GIBBS method. The first extracts the mechanical properties from automatic self-consistent stress-strain calculations, while the latter employs those mechanical properties to evaluate the thermodynamics within the Debye model. This new thermoelastic workflow is benchmarked against a set of 74 experimentally characterized systems to pinpoint a robust computational methodology for the evaluation of bulk and shear moduli, Poisson ratios, Debye temperatures, Gr\"uneisen parameters, and thermal conductivities of a wide variety of materials. The effect of different choices of equations of state and exchange-correlation functionals is examined and the optimum combination of properties for the Leibfried-Schl\"omann prediction of thermal conductivity is identified, leading to improved agreement with experimental results than the GIBBS-only approach. The framework has been applied to the AFLOW.org data repositories to compute the thermoelastic properties of over 3500 unique materials. The results are now available online by using an expanded version of the REST-API described in the Appendix.

On the time differential dual-phase-lag thermoelastic model

Abstract: This paper studies the time differential dual-phase-lag model of a thermoelastic material, where the elastic deformation is accompanied by thermal effects governed by a time differential equation for the heat flux with dual phase lags. This coupling gives rise to a complex differential system requiring a special treatment. Uniqueness and continuous dependence results are established for the solutions of the mixed initial boundary value problems associated with the model of the linear theory of thermoelasticity with dual-phase-lag for an anisotropic and inhomogeneous material. Two methods are developed in this paper, both being based on an identity of Lagrange type and of a conservation law applied to appropriate initial boundary value problems associated with the model in concern. The uniqueness results are established under mild constitutive hypotheses (right like those in the classical linear thermoelasticity), without any restrictions upon the delay times (excepting the class of thermoelastic materials for which the delay time of phase lag of the conductive temperature gradient is vanishing and the delay time in the phase lag of heat flux vector is strictly positive, when an ill-posed model should be expected). The continuous dependence results are established by using a conservation law and a Gronwall inequality, under certain constitutive restrictions upon the thermoelastic coefficients and the delay times.

Design of thermoelastic multi-material structures with graded interfaces using topology optimization

Abstract: A level set based shape and topology optimization framework is used to study the effect of graded interfaces in the optimization process of micro-architectured multi-materials. In contrast to previous studies interfaces are considered as smooth transition between phases instead of a sharp delimitation between two phases. A study on extreme thermoelastic properties of 2D isotropic composites is achieved and optimal design are presented. The study shows how taking into account smooth interfaces can influence the optimal design of these materials.

Study of damage evolution in composite materials based on the Thermoelastic Phase Analysis (TPA) method

Abstract: Standards and conventional procedures used for analysing fatigue damage in composite materials involve high experimental campaign costs due to time-consuming tests. This aspect becomes relevant for large structures where the cost of experimental setup tends to rise according to structure dimensions. In this regard, in recent years, efforts to produce fatigue characterisation of materials have made use of several experimental techniques, i.e. thermographic techniques. Most of these, however, refer to Standard specimens and laboratory equipment and set-up. Through the use of Thermography, in this work a new procedure has been developed which is capable of monitoring damage in GFRP composite material. The analysis of thermal signal in the frequency domain allows for the isolation of indexes which are related to the thermoelastic and dissipative heat sources. In particular, the phase of thermoelastic signal, associated with intrinsic dissipation processes occurring in the material, has been used to localize and assess the damaged areas in a quantitative manner. Moreover, the thermoelastic phase analysis leads to an evaluation of the endurance limit of composites. In fact, by comparing the results with those provided by the standard test methods, the potential has been shown of the proposed procedure firstly as a non-destructive technique for continuous monitoring of damage in composite structures undergoing fatigue loadings, and secondly, as a fatigue limit index.

Thermal stress analysis of functionally graded plates with temperature-dependent material properties using theory of elasticity

Abstract: Based on the three-dimensional elasticity theory, the transient thermal residual stress analyses of one-dimensional functionally graded rectangular plates (FGPs) have been performed under in-plane constant heat flux for different compositional gradient exponents. The thermo-mechanical properties of FGPs were assumed to be vary with a power law along an in-plane direction, not through the plate thickness direction and temperature-dependent/independent. The Heat Transfer and Navier's Equations in cartesian coordinates which represent the two-dimensional thermoelastic problem were resolved by means of the Finite-Difference Method (FDM), and the set of linear equations were solved using the pseudo singular value method. The effect of the coordinate derivatives of material properties were considered in both Heat Transfer and Navier's Equations. The current study aims at determining the effect of temperature dependence and temperature independence of material properties and the compositional gradient exponents in FGPs on the levels of temperature, strain and stress. The FGPs with temperature-dependent material properties showed higher levels of temperature, strain and stress than those with temperature-independent material properties. In order to verify the results of this study, two-dimensional thermo-elastic problem was resolved using the Finite Element Method (FEM) and the results are compared.

Transient response for a half-space with variable thermal conductivity and diffusivity under thermal and chemical shock

Abstract: The present work aims to investigate the transient thermoelastic diffusive response for a half-space with variable thermal conductivity and diffusivity in the context of the generalized thermoelastic diffusion theory. The boundary plane of the half-space is assumed to be traction free and subjected to a time-dependent thermal and chemical shock. The governing equations of the problem are formulated by using Kirchhoff’s transformation. Due to the complexity of the equations, Laplace transformation method is applied to solve them. Numerical results are obtained and illustrated graphically. Parameter studies are performed to evaluate the effects of variable thermal conductivity and diffusivity on the response. The present investigation could be helpful for better understanding the multifield coupling effect of mechanical and thermal fields in real materials.

Thermoelastic Dissipation in Micromachined Birdbath Shell Resonators

Abstract: Many MEMS gyroscopes rely on micro mechanical resonators to measure angular rotation. Maximizing their quality factor ( $Q$ ) will help improve accuracy. There are several energy dissipation mechanisms that limit $Q$ . This paper studies the role of thermoelastic dissipation (TED) in micro birdbath shell resonators. Fully coupled thermo-mechanical equations of physical behavior are solved for these shells using a finite-element method. Furthermore, an analytical model is developed to predict TED. The effects of material properties, shell geometry, edge chipping around the shell rim, trimming approaches, thin-film coatings, and operating temperature on thermoelastic $Q$ ( $Q_{{TED}})$ are studied. It is found that the shell material properties and rim thickness have significant impact on $Q_{{TED}}$ . However, edge chipping and most of the shell geometrical parameters do not have large impact. Additionally, this paper shows that some trimming approaches, such as forming grooves along the rim, can improve $Q_{{TED}}$ . A study of the effect of metal coatings on the resonator on $Q$ shows that the coating thickness and material are important factors affecting $Q$ and $Q_{{TED}}$ . The results presented in this paper provide guidelines for the design of other similar high- $Q$ resonators. [2016–0027]

Rayleigh surface wave propagation in orthotropic thermoelastic solids under three-phase-lag model

Abstract: The present article deals with the propagation of Rayleigh surface waves in a homogeneous, orthotropic thermoelastic half-space in the context of three-phase-lag model of thermoelasticity. The freq...

Thermomagnetic effect with two temperature theory for photothermal process under hydrostatic initial stress

Abstract: A novel technique is used to investigate the influence of magnetic field for a two dimensional deformations on a two temperature problem at the free surface of a semi-infinite medium. The investigation is carried out under the effects of both mechanical force and hydrostatic initial stress during a photothermal excitation theory. The equations of elastic waves, heat conduction equation, quasi-static electric field, carrier density, two temperature coefficient, ratios, and constitutive relationships for the thermo-magnetic-electric medium are obtained using the Harmonic Wave Method (HWM) technique. The effects of thermoelastic, thermoelectric and two temperature parameters of the applied force on the displacement component, force stress, carrier density and temperature distribution has been depicted graphically.

Ripple formation on silver after irradiation with radially polarised ultrashort-pulsed lasers

Abstract: We report on the morphological effects induced by the inhomogeneous absorption of cylindrically polarized femtosecond laser irradiation of silver (Ag) in sub-ablation conditions. A theoretical prediction of the role of surface plasmon excitation and thermal effects in the production of self-formed periodic ripples structures is evaluated. To this end, a combined hydrodynamical and thermoelastic model is presented to account for the influence of temperature-related lattice movements in laser beam conditions that are sufficient to produce material melting. The results indicate that material displacements due to hydrodynamics are substantially larger than strain-related movements, which also emphasises the predominant role of fluid transport in surface modification. Moreover, theoretical simulations highlight the influence of the polarisation state in the size of ripple periodicity for a specialized case of cylindrically polarized beams, the radially polarized beams. The results show that the ripple periodic...

Nonlocal thermoelasticity theory without energy dissipation for nano-machined beam resonators subjected to various boundary conditions

Abstract: A model of nonlocal thermoelasticity theory of Green and Naghdi without energy dissipation is used to consider the vibration behavior of a nano-machined resonator. The nonlocality brings in an internal length scale in the formulation and, thus, allows for the interpretation of size effects. The governing frequency equation is given for nanobeams subjected to different boundary conditions. A combination of simply-supported, clamped, and free boundary conditions is investigated. The effect of side-to-thickness and aspect ratios, as well as the influence of either nonlocal parameter or thermoelastic coupling are all investigated. In addition, the effect of environmental temperature T0 on the vibration frequency is also investigated.