Showing papers on "Thermoelastic damping published in 2009"

Thermoelasticity with Finite Wave Speeds

Abstract: Preface Introduction 1. Fundamentals of linear thermoelasticity with finite wave speeds 2. Formulations of initial-boundary value problems 3. Existence and uniqueness theorems 4. Domain of influence theorems 5. Convolutional variational principles 6. Central equation of thermoelasticity with finite wave speeds 7. Exact aperiodic-in-time solutions of Green-Lindsay theory 8. Kirchhoff type formulas and integral equations in Green- Lindsay theory 9. Thermoelastic polynomials 10. Moving discontinuity surfaces 11. Time-periodic solutions 12. Physical aspects and applications of hyperbolic thermoelasticity 13. Nonlinear hyperbolic rigid heat conductor of the Coleman type References Index

Energy decay rate of the thermoelastic Bresse system

Abstract: In this paper, we study the energy decay rate for the thermoelastic Bresse system which describes the motion of a linear planar, shearable thermoelastic beam. If the longitudinal motion and heat transfer are neglected, this model reduces to the well-known thermoelastic Timoshenko beam equations. The system consists of three wave equations and two heat equations coupled in certain pattern. The two wave equations about the longitudinal displacement and shear angle displacement are effectively damped by the dissipation from the two heat equations. Actually, the corresponding energy decays exponentially like the classical one-dimensional thermoelastic system. However, the third wave equation about the vertical displacement is only weakly damped. Thus the decay rate of the energy of the overall system is still unknown. We will show that the exponentially decay rate is preserved when the wave speed of the vertical displacement coincides with the wave speed of longitudinal displacement or of the shear angle displacement. Otherwise, only a polynomial type decay rate can be obtained. These results are proved by verifying the frequency domain conditions.

A thermodynamic approach to determine accurate potentials for molecular dynamics simulations: thermoelastic response of aluminum

Abstract: An accurate description of the thermoelastic response of solids is central to classical simulations of compression- and deformation-induced condensed matter phenomena. To achieve the correct thermoelastic description in classical simulations, a new approach is presented for determining interatomic potentials. In this two-step approach, values of atomic volume and the second- and third-order elastic constants measured at room temperature are extrapolated to T = 0 K using classical thermo-mechanical relations that are thermodynamically consistent. Next, the interatomic potentials are fitted to these T = 0 K pseudo-values. This two-step approach avoids the low-temperature quantum regime, providing consistency with the assumptions of classical simulations and enabling the correct thermoelastic response to be recovered in simulations at room temperature and higher. As an example of our approach, an EAM potential was developed for aluminum, providing significantly better agreement with thermoelastic data compared with previous EAM potentials. The approach presented here is quite general and can be used for other potential types as well, the key restriction being the inapplicability of classical atomistic simulations when quantum effects are important.

Dimensional considerations in achieving large quality factors for resonant silicon cantilevers in air

Abstract: This work aims to provide guidelines for designing rectangular silicon cantilever beams to achieve maximum quality factors for the fundamental flexural resonance at atmospheric pressure. The methodology of this work is based on experimental data acquisition of resonance characteristics of silicon cantilevers, combined with modification of analytical damping models to match the captured data. For this purpose, rectangular silicon cantilever beams with thicknesses of 5, 7, 8, 11, and 17 μm and lengths and widths ranging from 70 to 1050 μm and 80 to 230 μm, respectively, have been fabricated and tested. Combining the three dominant damping mechanisms, i.e., the air damping, support loss, and thermoelastic damping, the variation in the measured Q-factors with the cantilever geometrical dimensions is predicted. Also to better describe the experimental data, modified models for air damping have been developed. These modified models can predict the optimum length and thickness of a resonant cantilever to achieve...

Generalized thermoelastic functionally graded orthotropic hollow sphere under thermal shock with three-phase-lag effect

Abstract: This problem deals with the determination of thermo-elastic interaction due to step input of temperature on the boundaries of a functionally graded orthotropic hollow sphere in the context of linear theories of generalized thermo-elasticity. Using the Laplace transformation the fundamental equations have been expressed in the form of vector–matrix differential equation which is then solved by eigenvalue approach. The inverse of the transformed solution is carried out by applying a method of Bellman et al. Stresses, displacement and temperature distributions have been computed numerically and presented graphically in a number of figures. A comparison of the results for different theories (TEWOED(GN-II), TEWED(GN-III) and three-phase-lag model) is presented. When the material is homogeneous, isotropic and outer radius of the hollow sphere tends to infinity, the corresponding results agree with that of existing literature for GN-III model.

Thermoelastic analysis of a thick walled cylinder made of functionally graded piezoelectric material

Abstract: In this paper, the thermopiezoelectric behavior of a thick walled cylinder with functionally graded materials is studied. The cylinder is loaded under the temperature gradient and inner and outer pressures. All the mechanical, thermal and piezoelectric properties except the Poisson ratio can be expressed as a power function in the radial direction. In the first step, with the solution of the heat transfer equation, a symmetric distribution of temperature is obtained. The stresses and electric displacement relations can be derived in terms of the temperature, electric field and strain. Substituting the resultant relations into the mechanical and electrical equilibrium equations yields the system of nonhomogeneous differential equations with two unknown variables (the mechanical displacement and the electrical potential). Solving the system of nonhomogeneous differential equations yields other mechanical and thermal terms such as the stress, displacement, electric field and electric displacement. The main result of the present study is that, by applying a proper distribution of mechanical and thermal properties in the functionally graded piezoelectric material (FGPM) solid structures, the distributions of stresses, electric potential and electric field in the FGPM can be controlled. Hence, the FGPM can be used in sensors or actuators.

Multimode thermoelastic dissipation

Abstract: In this paper, we investigate thermoelastic dissipation (TED) in systems whose thermal response is characterized by multiple time constants. Zener [Phys. Rev. 52, 230 (1937)] analyzed TED in a cantilever with the assumption that heat transfer is one dimensional. He showed that a single thermal mode was dominant and arrived at a formula for quantifying the quality factor of a resonating cantilever. In this paper, we present a formulation of thermoelastic damping based on entropy generation that accounts for heat transfer in three dimensions and still enables analytical closed form solutions for energy loss estimation in a variety of resonating structures. We apply this solution technique for estimation of quality factor in bulk mode, torsional, and flexural resonators. We show that the thermoelastic damping limited quality factor in bulk mode resonators with resonator frequency much larger than the eigenfrequencies of the dominant thermal modes is inversely proportional to the frequency of the resonator unlike in flexural mode resonators where the quality factor is directly proportional to the resonant frequency. Purely torsional resonators are not limited by TED as the deformation is isochoric. We show that it is possible to express the quality factor obtained by full three-dimensional analyses as a weighted sum of Zener formula based modal quality factors. We analytically estimate the quality factor of a cantilever and a fixed-fixed beam and corroborate it with data to show that the assumption of a single dominant thermal mode, which is valid in one-dimensional analysis, is violated. The analytical formulation described in this paper permits estimation of energy lost due to heat transfer in orthogonal directions. It is found that the entropy generated due to heat transfer along the beam becomes significant in beams with aspect ratio (length/width) below 20.

Nonlinear damped Timoshenko systems with second sound—Global existence and exponential stability

Abstract: In this paper, we consider nonlinear thermoelastic systems of Timoshenko type in a one-dimensional bounded domain. The system has two dissipative mechanisms being present in the equation for transverse displacement and rotation angle—a frictional damping and a dissipation through hyperbolic heat conduction modelled by Cattaneo's law, respectively. The global existence of small, smooth solutions and the exponential stability in linear and nonlinear cases are established. Copyright © 2008 John Wiley & Sons, Ltd.

Fields of stored energy associated with localized necking of steel

Abstract: This paper describes an experimental procedure for the simultaneous determination of heat sources and mechanical energy involved locally during a heterogeneous tensile test. This procedure involves two complementary imaging techniques: digital image correlation (DIC) and infrared thermography (IRT). The first technique gives displacement fields from which strains are derived while the second provides temperature fields with which the heat sources are estimated using a local form of the heat equation. Moreover, a method based on integration of equilibrium equations under the plane stress assumption is used to determine the stress distribution during the test. The distribution of the local deformation energy developed by the material is then assessed using stress and strain-rate fields. Tensile tests were performed on thin flat steel samples. The results revealed early and gradual development of strain localization within the gauge part of the specimen. Energy balances were performed inside and outside the necking zone based on the assumption that the thermoelastic part of the behaviour remains linear and isotropic. Finally, indirect estimate of the stored energy led us to compute the time course of the local Taylor-Quinney coefficient. mechanical energy involved locally during a heterogeneous tensile test. This procedure involves two complementary imaging techniques: digital image correlation (DIC) and infrared thermography (IRT). The first technique gives displacement fields from which strains are derived while the second provides temperature fields with which the heat sources are estimated using a local form of the heat equation. Moreover, a method based on integration of equilibrium equations under the plane stress assumption is used to determine the stress distribution during the test. The distribution of the local deformation energy developed by the material is then assessed using stress and strain-rate fields. Tensile tests were performed on thin flat steel samples. The results revealed early and gradual development of strain localization within the gauge part of the specimen. Energy balances were performed inside and outside the necking zone based on the assumption that the thermoelastic part of the behaviour remains linear and isotropic. Finally, indirect estimate of the stored energy led us to compute the time course of the local Taylor-Quinney coefficient.

Uniqueness and Growth of Solutions in Two-Temperature Generalized Thermoelastic Theories

Abstract: In this work we study modifications of the non-classical models of thermoelasticity, the one proposed Green and Lindsay and the one stated by Lord and Shulman, to two-temperature setting. We prove uniqueness results for the solutions of the systems of equations that model both theories for isotropic material. We also provide growth estimates for the solutions.

Thermoelastic solution of a functionally graded variable thickness rotating disk with bending based on the first-order shear deformation theory

Abstract: A theoretical solution for thermoelastic analysis of functionally graded (FG) rotating disk with variable thickness based on first-order shear deformation theory (FSDT) is presented. Material properties and disk thickness profile are assumed to be represented by power law distributions. A semi analytical solution for displacement field is given under two types of boundary conditions applied for solid and annular disks. The effects of the material grading index and the geometry of the disk on the stress and displacement fields are investigated. Mechanical responses homogeneous disks versus FG disks are compared and verified with the known results in the literature. It is seen that the transverse displacements in FG solid disks with roller support condition at the outer surface remain between the minimum displacement value for the full-ceramic disk and the maximum displacement value for the full-metal disk. It is found that the transverse displacements in FG mounted disks with free condition at outer surface may not lie in between the displacement values for full-metal and full-ceramic disks. It is observed that the absolute moment resultant for FG mounted disk with concave profile is lowest compared to the FG mounted disk with linear or convex profile. It can be concluded that the gradation of the metal–ceramic components and the geometry of the disk are significant parameters in the thermomechanical responses of FG disks.

Thermoelastic analysis of functionally graded plates using the element-free kp-Ritz method

Abstract: In this paper, the static responses of metal and ceramic functionally graded plates subject to thermal and mechanical loads are investigated. The first-order shear deformation plate theory is adopted, and the displacement field is expressed in terms of a set of mesh-free kernel particle functions. It is assumed that the material property of each plate exponentially varies through the thickness. The governing equations are solved to obtain the plate displacements and axial stresses using the element-free kp-Ritz method. The effects of the volume fraction, material property, boundary conditions and length-to-thickness ratio on the plate deflection and axial stress are discussed in detail. The numerical results generated from the proposed method agree well with those in the literature.

Finite element analysis of two-temperature generalized magneto-thermoelasticity

Abstract: A general finite element model is proposed to analyze transient phenomena in thermoelastic solids. Youssef model of two-temperature generalized magneto-thermoelasticity is selected for an homogenous, isotropic, conducting and elastic medium, which is subjected to thermal shock, and a magnetic field with constant intensity acts tangent to the bounding plane. The numerical solution of the nondimensional governing partial differential equations of the problem has been shown graphically.

A finite element formulation for thermoelastic damping analysis

Abstract: We present a finite element formulation based on a weak form of the boundary value problem for fully coupled thermoelasticity. The thermoelastic damping is calculated from the irreversible flow of entropy due to the thermal fluxes that have originated from the volumetric strain variations. Within our weak formulation we define a dissipation function that can be integrated over an oscillation period to evaluate the thermoelastic damping. We show the physical meaning of this dissipation function in the framework of the well-known Biot's variational principle of thermoelasticity. The coupled finite element equations are derived by considering harmonic small variations of displacement and temperature with respect to the thermodynamic equilibrium state. In the finite element formulation two elements are considered: the first is a new 8-node thermoelastic element based on the Reissner–Mindlin plate theory, which can be used for modeling thin or moderately thick structures, while the second is a standard three-dimensional 20-node iso-parametric thermoelastic element, which is suitable to model massive structures. For the 8-node element the dissipation along the plate thickness has been taken into account by introducing a through-the-thickness dependence of the temperature shape function. With this assumption the unknowns and the computational effort are minimized. Comparisons with analytical results for thin beams are shown to illustrate the performances of those coupled-field elements. Copyright © 2008 John Wiley & Sons, Ltd.

A Thick Plate Problem in the Theory of Generalized Thermoelastic Diffusion

Abstract: In this work, the problem of a thermoelastic thick plate with a permeating substance in contact with one of the bounding planes is considered in the context of the theory of generalized thermoelastic diffusion with one relaxation time. The bounding surface of the half-space is taken to be traction free and is subjected to a time-dependent thermal shock. The chemical potential is also assumed to be a known function of time on the bounding plane. Laplace transform techniques are used. The solution is obtained in the Laplace transform domain by using a direct approach. The solution of the problem in the physical domain is obtained numerically using a numerical method for the inversion of the Laplace transform based on Fourier expansion techniques. The temperature, displacement, stress, and concentration as well as the chemical potential are obtained. Numerical computations are carried out and represented graphically.

Energy decay in a Timoshenko-type system with history in thermoelasticity of type III

Abstract: In this paper we consider a one-dimensional linear thermoelastic system of Timoshenko type with past history acting only in one equation. We consider the model where the heat conduction is given by Green and Naghdi's theories and prove exponential and polynomial stability results for the equal and nonequal wave-speed propagation. Our results are established under conditions on the relaxation function weaker than those in [9].

Study on the Use of Motion Compensation Techniques to Determine Heat Sources. Application to Large Deformations on Cracked Rubber Specimens

Abstract: This paper deals with the determination of the thermal response of elastomeric materials subjected to cyclic loading. In this case, the material undergoes large deformations, so a suitable motion compensation technique has been developed to track the material points and their temperature during the test. Special attention is paid to the Narcissus effect and to the detector matrix of the infrared camera used in the study. Heat sources are then derived from the temperature maps. The thermoelastic inversion phenomenon has been experimentally evidenced during a cyclic test performed on an elastomeric notched specimen. The heat source distribution close to the crack tip has also been deduced from the temperature maps, thus highlighting the relevance of the approach.

Thermoelastic Interactions on Two-Temperature Generalized Thermoelasticity in an Infinite Medium with a Cylindrical Cavity

Abstract: The present work is aimed at the study of thermoelastic interactions in an infinite medium with a cylindrical cavity in the context of a theory of generalized thermoelasticity in which the theory of heat conduction in deformable bodies depends on two different temperatures—conductive temperature and dynamic temperature. The cavity surface is assumed to be stress free and is subjected to a thermal shock. In order to make a comparison between the two-temperature generalized thermoelastic model and one-temperature generalized thermoelastic model the problem is formulated on the basis of two different models of thermoelasticity: namely, the Lord–Shulman model and the two temperature Lord–Shulman model in a unified way. Laplace transform technique and decoupling of coupled differential equations are used to derive the solution in transform domain which is then followed by the inversion of Laplace transform by a numerical method to obtain the solutions for field variables in the physical domain. Short-time appr...