Showing papers on "Thermoelastic damping published in 2000"

Thermoelastic damping in micro- and nanomechanical systems

Abstract: The importance of thermoelastic damping as a fundamental dissipation mechanism for small-scale mechanical resonators is evaluated in light of recent efforts to design high-Q micrometer- and nanometer-scale electromechanical systems. The equations of linear thermoelasticity are used to give a simple derivation for thermoelastic damping of small flexural vibrations in thin beams. It is shown that Zener’s well-known approximation by a Lorentzian with a single thermal relaxation time slightly deviates from the exact expression.

High-pressure lattice dynamics and thermoelasticity of MgO

Abstract: We present an ab initio study of the thermoelastic properties of MgO over a wide range of pressure and temperature. Phonon dispersions for equilibrium and strained configurations are obtained from density-functional perturbation theory. They are used to calculate thermodynamical potentials within the quasiharmonic approximation and several derived quantities of physical interest without further approximations. These include the temperature dependence of individual elastic constants at high pressures. Extensive and successful comparisons with experimental data demonstrate that the quasiharmonic approximation combined with ab initio phonon calculations provides an important theoretical approach for exploring thermodynamical properties of materials over a considerable pressure-temperature regime.

Nonlinear Waves in Elastic Crystals

Abstract: 1. DIFFERENT TYPES OF CRYSTAL 2. DISCRETE AND CONTINUUM DESCRIPTIONS: GENERAL INTRODUCTION 3. ELASTICITY AND ANELASTICITY: CONTINUOUS VIEWPOINT 4. ELASTICITY AND ANELASTICITY: DISCRETE VIEWPOINT 5. COUPLED FIELDS IN ELASTICITY 6. NONLINEAR WAVES IN ELASTIC CHAINS 7. NONLINEAR WAVES IN ELASTIC CRYSTALS WITH A MICROSTRUCTURE 8. NONLINEAR WAVES IN MARTENSITIC STRUCTURES 9. NONLINEAR ACOUSTIC SURFACE WAVES ON CRYSTALS 10. SHOCK WAVES AND PHASE-TRANSITION FRONTS IN THERMOELASTIC CRYSTALS 11. MISCELLANI 12. POSTFACE BY WAY OF CONCLUSION

Three-dimensional thermoelastic deformations of a functionally graded elliptic plate

Abstract: A new solution in closed form is obtained for the thermomechanical deformations of an isotropic linear thermoelastic functionally graded elliptic plate rigidly clamped at the edges. The through-thickness variation of the volume fraction of the ceramic phase in a metal–ceramic plate is assumed to be given by a power-law type function. The effective material properties at a point are computed by the Mori–Tanaka scheme. It is found that the through-thickness distributions of the in-plane displacements and transverse shear stresses in a functionally graded plate do not agree with those assumed in classical and shear deformation plate theories.

Thermoelastic noise and homogeneous thermal noise in finite sized gravitational-wave test masses

Abstract: An analysis is given of thermoelastic noise (thermal noise due to thermoelastic dissipation) in finite sized test masses of laser interferometer gravitational-wave detectors. Finite-size effects increase the thermoelastic noise by a modest amount; for example, for the sapphire test masses tentatively planned for LIGO-II and plausible beam-spot radii, the increase is ≲10 percent. As a side issue, errors are pointed out in the currently used formulas for conventional, homogeneous thermal noise (noise associated with dissipation which is homogeneous and described by an imaginary part of the Young’s modulus) in finite sized test masses. Correction of these errors increases the homogeneous thermal noise by ≲5 percent for LIGO-II-type configurations.

Eigenvalue solution of thermoelastic instability problems using Fourier reduction

Abstract: A › nite-element method is developed for determining the critical sliding speed for thermoelastic instability of an axisymmetric clutch or brake. Linear perturbations on the constant-speed solution are sought that vary sinusoidally in the circumferential direction and grow exponentially in time. These factors cancel in the governing thermoelastic and heat-conduction equations, leading to a linear eigenvalue problem on the two-dimensional cross-sectional domain for the exponential growth rate for each Fourier wavenumber. The imaginary part of this growth rate corresponds to a migration of the perturbation in the circumferential direction. The algorithm is tested against an analytical solution for a layer sliding between two half-planes and gives excellent agreement, for both the critical speed and the migration speed. Criteria are developed to determine the mesh re› nement required to give an adequate discrete description of the thermal boundary layer adjacent to the sliding interface. The method is then used to determine the unstable mode and critical speed in geometries approximating current multi-disc clutch practice.

Thermoelastic Damping in Micro- and Nano-Mechanical Systems.

Abstract: The importance of thermoelastic damping as a fundamental dissipation mechanism for small-scale mechanical resonators is evaluated in light of recent efforts to design high-Q micrometer- and nanometer-scale electromechanical systems. The equations of linear thermoelasticity are used to give a simple derivation for thermoelastic damping of small flexural vibrations in thin beams. It is shown that Zener’s well-known approximation by a Lorentzian with a single thermal relaxation time slightly deviates from the exact expression.

Grüneisen parameters and isothermal equations of state

Abstract: The Gruneisen parameter (fl is of considerable importance to Earth scientists because it sets limitations on the thermoelastic properties of the lower mantle and core. However, there are several formulations of the Gruneisen parameter in frequent use which nor only give different values for gamma at ambient pressure but also predict a varying dependence of gamma as a function of compression. The Gruneisen parameter is directly related to the equation of state (EOS), yet it is often the case that both the form of gamma and the EOS are chosen independently of each other and somewhat arbitrarily. In this paper we have assessed some of the more common definitions of the Gruneisen parameter and the EOS, and have applied them to a test material. OF the EOS considered, when compared against ab initio compressional data for hcp-Fe as our exemplar, we find that the fourth order logarithmic and Vinet relations describe the material with the highest accuracy. Of the expressions for gamma considered it has been suggested, on theoretical grounds, that the modified free-volume formulation should be expected to give the most realistic description of the thermoelastic behavior of a material. However, when we use the fourth order logarithmic EOS to obtain the compressional behavior of the various Gruneisen parameters, we find that there is, in fact, poor agreement between the modified free-volume formulation and the Mie-Gruneisen parameter obtained directly from ab initio free energy calculations on hcp-Fe. We conclude that none of the analytical forms of gamma are sufficiently sophisticated to describe the thermoelastic behavior of real materials with great accuracy, and care must therefore be taken when attempting to model the thermoelastic behavior of solids to ensure that the appropriate gamma (ideally obtained from experiments or ab initio calculations) and equations of state are used.

Stress-free two-way thermoelastic shape memory and field-enhanced strain in Ni52Mn24Ga24 single crystals

Abstract: Stress-free and two-way thermoelastic shape memory, with 1.2% strain and 6 K temperature hysteresis, has been found in single crystalline Ni52Mn24Ga24. The deformation can be enhanced more than three times, up to 4.0% shrinkage with a bias field 1.2 T applied along the measurement direction, or changed to 1.5% expansion by the 1.2 T applied perpendicular to the measurement direction. For achieving a large deformation, the magnetic field exhibits a more evident contribution than an external stress on this material. These characteristics can be attributed to the low level of internal stress and the preferential orientation of the martensitic variants.

A New Thermoelastic Model for Analysis of Shape Memory Alloy Hybrid Composites

Abstract: A constitutive model and a finite element formulation are developed for predicting the thermomechanical response of SMA hybrid composite structures subjected to combined thermal and mechanical load...

The reflection phenomena of sv-waves in a generalized thermoelastic medium

Abstract: We discuss the reflection of thermoelastic plane waves at a solid half-space nearby a vacuum. We use the generalized thermoelastic waves to study the effects of one or two thermal relaxation times on the reflection plane harmonic waves. The study considered the thermal and the elastic waves of small amplitudes in a homogeneous, isotropic, and thermally conducting elastic solid. The expressions for the reflection coefficients, which are the ratio of the amplitudes of the reflected waves to the amplitude of the incident waves are obtained. It has been shown, analytically, that the elastic waves are modified due to the thermal effect. The reflection coefficients of a shear wave that incident from within the solid on its boundary, which depend on the thermoelastic coupling factor and included the thermal relaxation times, have been found in the general case. The numerical values of reflection coefficients against the angle of incidence for different values of thermal relaxation times have been calculated and the results are given in the form of graphs. Some special cases of reflection have also been discussed, for example, in the absence of thermal effect our results reduce to the ordinary pure elastic case.

A Transient Thermoelastohydrodynamic Study of Steadily Loaded Plain Journal Bearings Using Finite Element Method Analysis

Abstract: The present paper proposes an advanced bidimensional model necessary to calculate the temperature field in a journal bearing submitted to both rapid and slow start-ups. The model takes into account realistic thermal boundary conditions at fluid film-solid interfaces. The thermoelastic deformations of both the journal and of the bush are also considered and a special attention is paid to the ruptured zone of the film. The Finite Element Method (with upwind techniques whenever necessary) is employed to solve the equations implied by the model. Finally, the theoretical predictions were validated by comparison with experimental data.

Damping Investigations of a Simplified Frictional Shear Joint

Abstract: The inability to include accurate damping models for bolted connections limits the accuracy of structural models to predict dynamic response. Experiments utilizing a system simulating a bolted shear joint to investigate frictional damping associated with micro-slip are discussed. Measurement and three computational techniques to quantify the energy dissipation as a function of the applied force to the shear joint are described. Parameters of the shear joint include the normal force amplitude and distribution, input force, frequency, material type, and surface characteristics. An underlying power law relationship between the energy dissipated per cycle and the applied input force is revealed and explored for the simplified shear joint. Methods to directly observe and measure the damping force at resonance are also discussed. This is a continuation of the work that was presented last year.

Generalized thermoelastic waves in homogeneous isotropic plates

Abstract: The propagation of thermoelastic waves in homogeneous isotropic plate subjected to stress-free and rigid insulated and isothermal conditions is investigated in the context of conventional coupled thermoelasticity (CT), Lord–Shulman (LS), Green–Lindsay (GL), and Green–Nagdhi (GN) theories of thermoelasticity. Secular equations for the plate in closed form and isolated mathematical conditions for symmetric and skew-symmetric wave mode propagation in completely separate terms are derived. It is shown that the motion for SH modes gets decoupled from the rest of the motion and remains unaffected due to thermo-mechanical coupling and thermal relaxation effects. The phase velocities for SH modes have also been obtained. The results for coupled and uncoupled theories of thermoelasticity have been obtained as particular cases from the derived secular equations. At short wavelength limits the secular equations for symmetric and skew-symmetric waves in a stress-free insulated and isothermal plate reduce to Rayleigh surface waves frequency equations. Finally, the numerical solution is carried out for aluminum–epoxy composite material and the dispersion curves for symmetric and skew-symmetric wave modes are presented to illustrate and compare the theoretical results.

Effects of thermal relaxations on thermoviscoelastic interactions in an unbounded body with a spherical cavity subjected to a periodic loading on the boundary

Abstract: Thermoviscoelastic interactions in an infinite homogeneous viscoelastic medium with a spherical cavity are studied. The cavity surface is subjected to a periodic loading and zero temperature change. The classical dynamical theory of thermoelasticity as well as the generalized theories of thermoelasticity are applied to consider the thermoelastic coupling. The analytical expressions for the closed-form solutions of displacement, temperature, and stresses are obtained; and the thermal relaxation effects on the interactions are studied to compare the three theories. The numerical values of the physical quantities are computed for a suitable material. The results are presented graphically to illustrate the problem.

Boundary element analysis of coupled thermoelasticity with relaxation times in finite domain

Abstract: A boundary element method based on the Laplace technique is developed for transient coupled thermoelasticity problems with relaxation times in a two-dimensional finite domain. The dynamic thermoelastic model of Green and Lindsay (Green, A. E., and Lindsay, K. E., Thermoelasticity, Journal of Elasticity, Vol. 2, No. 1, 1972, pp. 1-7) and Lord and Shulman (Lord, H. W., and Shulman, Y., A Generalized Dynamic Theory of Thermoelasticity, Journal of the Mechanics and Physics of Solids, Vol. 15, 1967, pp. 299-309) are selected. The Laplace transform method is applied in the time domain, and the resulting equations in the transformed field are discretized using a boundary element method. The nodal dimensionless temperature and displacements in the transformed domain are inverted to obtain the actual physical quantities, using the numerical inversion of the Laplace transform method. The concern is with thermoelastic waves detection, propagation, and reflection in a finite domain that have not been reported on in the past. Comparison is made with other solutions, and coupling and relaxation time effects in stress, displacement, and temperature distribution are investigated. Details of the formulation and numerical implementation are presented.

BEM analysis of thermal and mechanical shock in a two-dimensional finite domain considering coupled thermoelasticity

Abstract: A boundary element method based on the Laplace-transform technique is developed for transient coupled thermoelasticity problems of two-dimensional finite domain The Laplace-transform method is applied to the time domain and the resulting equations in the transformed field are discretized using the boundary element method The nodal dimensionless temperature and displacements in the transformed domain are inverted to obtain the actual physical quantities, using the numerical inversion of the Laplace-transform method The work is concerned with the thermal and mechanical shocks in a finite domain considering classical coupled theory of thermoelasticity Elastic and thermoelastic wave creation and propagation in a finite domain and their effects on each other are investigated Numerical implementations are presented and compared with the known data

Photoacoustic effect in stressed elastic solids

Abstract: A multimode approach based on the simultaneous application of several photothermal and photoacoustic methods is proposed for the study of thermal and thermoelastic effects in solids with residual stress. It includes photoacoustic gas microphone, photodeflection, photoreflectance and photoacoustic piezoelectric microscopy methods. This approach provides complementary information about thermal, elastic and thermoelastic properties of samples with residual stress. Some experimental results obtained within the framework of this approach for Vickers indentation zones in silicon nitride ceramic are presented. The model of the photoacoustic thermoelastic effect in solids with residual stress is proposed. It is based on the modified Murnaghan model of nonlinear elastic bodies which takes into account a possible dependence of the thermoelastic constant on stress. It is demonstrated that the developed theoretical model for the photoacoustic piezoelectric effect agrees qualitatively with the available experimental data.

Thermoelastic behaviour of hexagonal graphite-like boron nitride

Abstract: A synchrotron X-ray diffraction study on hexagonal graphite-like boron nitride (h-BN) was performed under high pressures and temperatures. From the measured P-V-Trelation for h-BN (with a three-dimensional ordering parameter P3 = 0.9) in the temperature range from 298 to 1273 K and up to 6.7 GPa, the thermoelastic parameters are derived by fitting a modified high temperature Birch-Murnaghan equation of state. The results are: bulk modulus B0[GPa] = 27.6-0.0081(T[K]-298) and its pressure derivative B1 = 10.5 + 0.0016(T [K] - 298). These values are for samples with P3 = 0.9 and are quite different for samples with different values of the order parameter. This parameter is shown to have a leading role in the determination of the thermoelastic properties of h-BN, which explains and reconciles the differences between previous results.