Showing papers on "Thermoelastic damping published in 1999"

Semigroups Associated with Dissipative Systems

Abstract: Preliminaries Some Definitions C0-Semigroup Generated by Dissipative Operator Exponential Stability and Analyticity The Sobolev Spaces and Elliptic Boundary Value Problems Linear Thermoelastic Systems The Setting of Problems for the One-Dimensional Thermoelastic System The Exponential Stability for the Dirichlet Boundary Conditions at Both Ends The Exponential Stability for the Stress-Free Boundary Conditions at Both Ends The Exponential Stability for the Stress-Free Boundary Conditions at One End The Thermoelastic Kirchhoff Plate Equations Linear Viscoelastic System Linear Viscoelastic System Wave Equation with Locally Distributed Damping Linear Viscoelastic System with Memory The Linear Viscoelastic Kirchoff Plate with Memory Linear Thermoviscoelastic Systems Linear One-Dimensional Thermoviscoelastic System Linear Three-Dimensional Thermoviscoelastic System with Memory Elastic Systems with Shear Damping Shear Diffusion Equations Laminated Beam with Shear Damping Linear Elastic Systems with Boundary Damping Second-Order Hyperbolic Equation Euler-Bernoulli Beam Equation Uniformly Stable Approximations Main Theorem Approximations of the Thermoelastic System Approximation of the Viscoelastic System Bibliography

Thermoelastic analysis of functionally graded ceramic-metal cylinder

Abstract: The pseudodynamic thermoelastic response of functionally graded ceramic-metal cylinders is studied. This paper presents the finite-element formulation of the 1D, axisymmetric heat transfer equation and the thermoelastic radial boundary value problem. A two-step solution of the governing equations of thermoelasticity is presented. Thermoelastic coupling is considered by taking into effect the temperature dependence of the constitutive equations. Nonlinearity due to the temperature dependence of the material properties of the constituent ceramic and metal is considered. A parametric study with respect to varying volume fraction of the metal is conducted. Temperature and radial/hoop stress distributions arising due to rapid heating of the inner surface of the functionally graded cylinder are presented.

A new theoretical approach to photoacoustic signal generation

Abstract: From the various mechanisms of photoacoustic (PA) signal generation, the one due to local thermal expansion in aqueous media is treated here in detail. This mechanism is also referred to as thermoelastic PA signal generation. A new physical explanation of the spherical PA profile is presented, from which the signals generated by other source geometries and temporal profiles can be deduced. The characteristic PA signal profiles are discussed for some fundamental and practical source geometries. Also the PA signal attenuation and deformation due to viscous and thermoelastic losses is discussed. The analytic result for the transient generated by a spherical Gaussian spatiotemporal PA source is presented. Experimental PA signals are shown for several geometries and source diameters.

On singular surfaces in isotropic linear thermoelasticity with initial stress

Abstract: It will be shown that the theory of a fundamental paper of Chadwick and Powdrill on singular surfaces, propagating in a linear thermoelastic body which is stress-free, homogeneous, and isotropic, also holds when the medium is subjected to hydrostatic initial stress provided the two characteristic speeds are suitably changed. The result is obtained by using Biot’s linearization of the constitutive law for the stress.

Dynamics of SDOF Systems with Nonlinear Viscous Damping

Abstract: The effects of nonlinear viscous damping on the dynamic response of single-degree-of-freedom (SDOF) structural systems are analyzed. This kind of damping characterizes a special class of fluid viscous dampers recently utilized in the field of vibration control as base-isolation devices or viscoelastic elements included in steel braces of framed structures. The analytical relationship adopted to reproduce the mechanical behavior of the fluid viscous dampers is a fractional power-law of the velocity, the exponent of which ranges between 0.1 and 0.2. This function had been previously calibrated on the results of a special experimental survey carried out at the University of Florence. The dynamics of the classical linear-viscous SDOF oscillator is herein reformulated on the basis of the above-mentioned fractional viscous damping (FrVD) relationship. In particular, the transient and steady-state responses are examined in both free and forced vibration conditions. The magnification and transmissibility factors are analytically determined for different damping levels. Moreover, the relation between the viscous damping coefficient and the frequency ratio (i.e., the ratio of the dynamic load to the oscillator frequencies) is defined. The diagrams describing these functions provide direct correlations between the damping as well as the elastic properties of the system and the frequency content of the dynamic action.

Introduction to thermoelastic stress analysis

Abstract: The theory of thermoelastic stress analysis is reviewed and the assumptions in developing the theory are assessed. The equipment for thermoelastic stress analysis is based on infra-red detection systems. The commercially available systems are described and appraised. Techniques for calibrating the output from the detectors are also provided.

Thermoelasticity for the analysis of crack tip stress fields — a review

Abstract: A comprehensive review is given of methods to determine the stress intensity factor at crack tips using thermoelastic stress analysis. In order to obtain accurate results a number of areas of experimental procedure need to be considered and these are discussed in detail. The paper concludes with a discussion on the future potential of the use of thermoelasticity for the analysis of cracks.

Uniform decay rates for full von karman system of dynamic theromelasticity with free boundary conditions and partial boundary dissipation

Abstract: The full von Karman system accounting for in plane acceleration and thermal effects is considered. The main results of the paper are: (i) the wellposedness of regular and weak (finite energy) solutions, (ii) the uniform decay rates obtained for the energy function in the presence of boundary damping affecting only the velocity field representing in plane displacements of the plate. The key role in these results is played by: (i) new sharp regularity estimates for the boundary traces of elastic systems and (ii) newly established properties of analyticity of semigroups arising in thermoelastic systems with free boundary conditions.

On the thermodynamics of thermoelastic materials with additional scalar degrees of freedom

Abstract: This work deals with the thermodynamic formulation of a model for a class of materials containing microstructure which evolves or changes relative to\/ the (global) bulk material. The approach taken here is based on a generalization of the total energy, total energy flux, and total energy supply to take into account the corresponding additional degrees of freedom involved. Restricting attention for simplicity to thermoelastic materials with scalar-valued such degrees of freedom, the thermodynamically-consistent forms of the remaining balance and corresponding constitutive relations for this material class are obtained in the context of the Muller-Liu entropy principle. In particular, the thermodynamically-consistent form of the evolution relation for the additional scalar-valued degrees of freedom obtained in this fashion contains in part\/ the well-known generalized Euler-Lagrange or Ginzburg-Landau relations established in many previous work, with the remaining terms accounting for effects associated with microinertia, or with non-equilibrium processes.

Effect of Geometry on Thermoelastic Instability in Disk Brakes and Clutches

Abstract: The finite element method is used to reduce the problem of thermoelastic instability (TEI) for a brake disk to an eigenvalue problem for the critical speed. Conditioning of the eigenvalue problem is improved by performing a preliminary Fourier decomposition of the resulting matrices. Results are also obtained for two-dimensional layer and three-dimensional strip geometries, to explore the effects of increasing geometric complexity on the critical speeds and the associated mode shapes. The hot spots are generally focal in shape for the three-dimensional models, though modes with several reversals through the width start to become dominant at small axial wavenumbers n, including a thermal banding mode corresponding to n = 0. The dominant wavelength (hot spot spacing) and critical speed are not greatly affected by the three-dimensional effects, being well predicted by the two-dimensional analysis except for banding modes. Also, the most significant deviation from the two-dimensional analysis can be approximated as a monotonic interpolation between the two-dimensional critical speeds for plane stress and plane strain as the width of the sliding surface is increased. This suggests that adequate algorithms for design against TEI could be developed based on the simpler two-dimensional analysis.

Derivation of systems of fundamental equations for a three-dimensional thermoelastic field with nonhomogeneous material properties and its application to a semi-infinite body

Abstract: A method of analytical development of three-dimensional thermoelastic problems for a medium with nonhomogeneous material properties is developed in this article. Assuming that the shear modulus elasticity G, the thermal conductivity lambda, and the coefficient of linear thermal expansion alpha vary with the power product form of axial coordinate variable z and introducing two kinds of displacement functions and the thermoelastic displacement function, the system of fundamental differential equations for such a three-dimensional field is established. As an illustrative example, we consider the thermoelastic problem of a semi-infinite body. The three-dimensional temperature solution in a steady state is obtained and the associated components of thermal displacement and stress are evaluated theoretically. Numerical calculations are carried out for several cases taking into account the variety of the nonhomogeneous material properties of G, lambda, and alpha, and these results are shown graphically.

Exact boundary integral transformation of the thermoelastic domain integral in BEM for general 2D anisotropic elasticity

Abstract: In the direct formulation of the boundary element method, body-force and thermal loads manifest themselves as additional volume integral terms in the boundary integral equation. The exact transformation of the volume integral associated with body-force loading into surface ones for two-dimensional elastostatics in general anisotropy, has only very recently been achieved. This paper extends the work to treat two-dimensional thermoelastic problems which, unlike in isotropic elasticity, pose additional complications in the formulation. The success of the exact volume-to-surface integral transformation and its implementation is illustrated with three examples. The present study restores the application of BEM to two-dimensional anisotropic elastostatics as a truly boundary solution technique even when thermal effects are involved.

Thermoelastic analysis of periodic thin lines deposited on a substrate

Abstract: Thermoelastic stresses and curvatures arising from patterned thin lines on initially flat isotropic substrates are analyzed. A connection is made between substrates with patterned lines and laminated anisotropic composites containing transverse matrix cracks. Using this analogy along with anisotropic plate theories, approximate analytical expressions are derived for volume-averaged stresses as well as curvatures along and normal to the lines, for any thickness, width and spacing of the lines. The predictions of the analysis are shown to compare favorably with finite element simulations of stresses and curvatures for Si substrates with Al, Cu or SiO 2 lines. The predictions also match prior experimental measurements of curvatures along and normal to patterned SiO 2 lines on Si wafers, and further capture the general experimental trends reported previously for curvature evolutions in Si wafers with Al lines. The model presented here thus provides a very convenient and simple analytical tool for extracting stresses in thin lines on substrates from a knowledge of experimentally determined film stress, thereby circumventing the need for detailed computations for a wide range of unpassivated line geometries of interest in microelectronic applications.

Applications of thermoelastic stress analysis to composite materials

Abstract: A number of applied thermoelastic stress analysis (TSA) studies on composite components and assemblies are described, for the purpose of illustrating the potential of the technique for use with composite materials.

Quantitative theory for laser-generated Lamb waves in orthotropic thin plates

Abstract: A quantitative theory for modeling the laser-generated transient ultrasonic Lamb waves propagating along arbitrary directions in orthotropic thin plates is presented by employing an expansion method of the generalized Lamb wave modes The displacement is expressed by a summation of the symmetric and antisymmetric modes in the surface stress-free orthotropic plate, and it is particularly appropriate for wave form analyses of Lamb wave in thin plates because one needs only to evaluate a few of the lowest order modes The transient wave forms are analyzed in the thermoelastic regime and the oil coating generation method for a transversely isotropic plate The results show that the theory provides a quantitative analysis to characterize anisotropic properties and elastic stiffness properties of the orthotropic plates by the laser-generated Lamb wave detection

A Thermoelastic Asperity Contact Model Considering Steady-State Heat Transfer

Abstract: One of the important issues in mixed lubrication is the contact problem involving frictional heating in the interface of contacting bodies. Due to contact and rubbing, temperature in the solid media varies, causing the contact conditions to change as a consequence of thermal distortion. A thermoelastic model for rough surfaces is developed for asperity contact subject to steady-state heat transfer. In this model, asperity distortion due to thermal and elastic-plastic deformations is considered. The thermal deformation is related to the contact pressure through a thermal influence function. Matrices for thermal and elastic influence functions are solved with the finite element method and the contact problem is computed with a mathematical programming method. Numerical analyses on the thermoelastic contact involving a rough surface reveal that asperity thermal distortion affects the contact pressure and surface separation at high frictional heat and deep asperity penetration. Presented at the 54th Annual Me...

Thermoelastic properties of plain weave composites for multilayer circuit board applications

Abstract: The thermoelastic properties of several common woven glass/epoxy substrate materials were characterized in both the warp and fill directions. Five common commercially pressed consisted of either one or two plies of C-staged woven glass epoxy substrate sandwiched between 1 ounce copper cladding. After the copper was removed from the cores, samples were cut for either mechanical property characterization or microstructural analysis with the test axis lying along either the warp or fill direction. The crimp angle and relative fiber volume fraction of each fabric was first determined from photomicrographs of polished cross-sections. Next, Young's modulus was measured via standard tension tests at room temperature. The storage and loss moduli were then measured as function of temperature using dynamic mechanical analysis (DMA). Finally, the coefficients of thermal expansion were determined using constant force thermal mechanical analysis (TMA) measurements. All of the substrates showed significant differences in microstructure and material properties between the warp and fill directions. Most of the laminates had a much lower crimp angle in the warp direction, which resulted in a higher modulus and lower coefficient of thermal expansion than the fill direction. Of the cores investigated, the properties of 3313 were the most balanced.

Pulsed top-hat beam thermal-lens measurement for ultraviolet dielectric coatings.

Abstract: A mode-mismatched surface thermal-lens technique with pulsed top-hat beam excitation and a near-field detection scheme are developed to measure in situ the thermoelastic response of ultraviolet dielectric coatings to excimer-laser (193- or 248-nm) irradiation The thermal-lens technique is demonstrated to be not only convenient for accurate determination of the laser-induced damage threshold (LIDT) but also sensitive to measurement of the thermoelastic response of dielectric coatings irradiated with fluence far below the LIDT, and hence is shown to be appropriate for time-resolved predamage investigation A minimum detectable surface displacement of approximately 0002 nm is achieved with a simple experimental configuration Nonlinear absorption as well as the nonlinear effect in laser conditioning of a LaF3/MgF2 highly reflective dielectric coating are observed for what is believed to be the first time

Thermoelasticity and contact

Abstract: Thermoelastic deformations can have a significant effect on the contact between elastic bodies, particularly in cases where the thermal boundary conditions at the interface are influenced by the contact pressure. In the classical Hertzian problem, the size of the contact area depends on the magnitude and direction of heat flow between the bodies. Idealized thermal boundary conditions can lead to ill-posed steady-state problems, but this difficulty is resolved by assuming a pressure-dependent thermal contact resistance. Steady states of the system can be unstable even when they are unique, in which case the behavior is either oscillatory or involves the steady motion of a contact pressure wave along the interface. Analytical and numerical perturbation methods have been developed to investigate the stability problem. These results find applications in heat transfer processes involving solid-solid contact, including the solidification of castings. In brakes and clutches, the heat generated at the sliding int...

Pendulum Mode Thermal Noise in Advanced Interferometers: A comparison of Fused Silica Fibers and Ribbons in the Presence of Surface Loss

Abstract: The use of fused-silica ribbons as suspensions in gravitational wave interferometers can result in significant improvements in pendulum mode thermal noise. Surface loss sets a lower bound to the level of noise achievable, at what level depends on the dissipation depth and other physical parameters. For LIGO II, the high breaking strength of pristine fused silica filaments, the correct choice of ribbon aspect ratio (to minimize thermoelastic damping), and low dissipation depth combined with the other achievable parameters can reduce the pendulum mode thermal noise in a ribbon suspension well below the radiation pressure noise. Despite producing higher levels of pendulum mode thermal noise, cylindrical fiber suspensions provide an acceptable alternative for LIGO II, should unforeseen problems with ribbon suspensions arise.