Showing papers on "Thermoelastic damping published in 1997"

Design of materials with extreme thermal expansion using a three-phase topology optimization method

Abstract: Composites with extremal or unusual thermal expansion coefficients are designed using a three-phase topology optimization method. The composites are made of two different material phases and a void phase. The topology optimization method consists in finding the distribution of material phases that optimizes an objective function (e.g. thermoelastic properties) subject to certain constraints, such as elastic symmetry or volume fractions of the constituent phases, within a periodic base cell. The effective properties of the material structures are found using the numerical homogenization method based on a finite-element discretization of the base cell. The optimization problem is solved using sequential linear programming. To benchmark the design method we first consider two-phase designs. Our optimal two-phase microstructures are in fine agreement with rigorous bounds and the so-called Vigdergauz microstructures that realize the bounds. For three phases, the optimal microstructures are also compared with new rigorous bounds and again it is shown that the method yields designed materials with thermoelastic properties that are close to the bounds. The three-phase design method is illustrated by designing materials having maximum directional thermal expansion (thermal actuators), zero isotropic thermal expansion, and negative isotropic thermal expansion. It is shown that materials with effective negative thermal expansion coefficients can be obtained by mixing two phases with positive thermal expansion coefficients and void.

Reflection and refraction of thermoelastic waves at an interface of two semi-infinite media with two relaxation times

Abstract: The reflection and refraction of thermoelastic waves at an interface of two semi-infinite media in contact with two relaxation times are studied following Green and Lindsay's theory. The analytical expressions for the partition of energy are carried out. The results for various values of the angle of incidence for the partition of energy are presented in the context of two different cases: (i) liquid-liquid and (ii) liquid-solid. The numerical results are represented graphically to aid the comparison with Lord and Shulman's theory in order to see the effect of the second relaxation time.

A new generation of boundary element methods in fracture mechanics

Abstract: In this paper the dual boundary element methods for the analysis of crack problems in fracture mechanics is presented. The formulations described include: elastostatic, thermoelastic, elastoplastic and elastodynamic. Also presented are formulations relating to anisotropic and concrete materials. Particular attention is given to crack growth modelling. Examples are presented to demonstrate the capability and robustness of this new generation of boundary element methods.

Thermoelastic equation of state of jadeite NaAlSi2O6: An energy‐dispersive Reitveld Refinement Study of low symmetry and multiple phases diffraction

Abstract: We report the first measurement of a complete set of thermoelastic equation of state of a clinopyroxene mineral. We have conducted an in situ synchrotron x-ray diffraction study of jadeite at simultaneous high pressures and high temperatures. A modified Rietveld profile refinement program has been applied to refine the diffraction spectra of low symmetry and multiple phases observed in energy dispersive mode. Unit cell volumes, measured up to 8.2 GPa and 1280 K, are fitted to a modified high-temperature Birch-Murnaghan equation of state. The derived thermoelastic parameters of the jadeite are: bulk modulus K=125 GPa with assumed pressure derivative of bulk modulus K′ = ∂K/∂P = 5.0, temperature derivative of bulk modulus , and volumetric thermal expansivity α = a + bT with values of a=2.56×10−5K−1 and b=0.26x10−8 K−2. We also derived thermal Gruneisen parameter γth=1.06 for ambient conditions; Anderson-Gruneisen parameter δTo=5.02, and pressure derivative of thermal expansion ∂α/∂P = −1.06×10−6 K−1 GPa−1. From the P-V-T data and the thermoelastic equation of state, thermal expansions at five constant pressures of 1.0, 2.5, 4.0, 5.5, and 7.5 GPa are calculated. The derived pressure dependence of thermal expansion is: Δα/ΔP = −0.97×10−6K−1GPa−1, in good agreement with the thermodynamic relations.

Dynamic analysis and damping of composite structures embedded with viscoelastic layers

Abstract: In recent years, it has been found that composites co-cured with viscoelastic materials can enhance the damping capacity of a composite structural system with little reduction in stiffness and strength. Because of the anisotropy of the constraining layers, the damping mechanism of co-cured composites is quite different from that of conventional structures with metal constraining layers. This paper presents an analysis of the dynamic properties of multiple damping layer, laminated composite beams with anisotropic stiffness layers, by means of the finite element-based modal strain energy method. ANSYS 4.4A finite element software has been used for this study. The variation of resonance frequencies and modal loss factors of various beam samples with temperature is studied. Some of these results are compared with the closed-form theoretical results of an earlier published work. For obtaining optimium dynamic properties, the effects of different parameters, such as layer orientation angle and compliant layering, are studied. Also, the effect of using a combination of different damping materials in the system for obtaining stable damping properties over a wide temperature range is studied.

Exponential stability and analyticity of abstract linear thermoelastic systems

Abstract: This paper develops an abstract framework for analysis of linear thermoelastic systems. Linear semigroup theory is used to establish the well-posedness. Sufficient conditions for the exponential stability and analyticity of the associated semigroups for the thermoelastic systems are obtained via the frequency domain method and a contradiction argument. The results are applied to linear thermoelastic rods, beams and plates of homogeneous and nonhomogeneous material with various boundary conditions.

Finite element analysis of frictionally excited thermoelastic instability

Abstract: The frictional heat generated during braking causes thermoelastic distortion that modifies the contact pressure distribution. If the sliding speed is sufficiently high, this can lead to frictionalfy excited thermoelastic instability, characterized by major nonuniformi-ties in pressure and temperature. In automotive applications, a particular area of concern is the relation between thermoelasticalfy induced hot spots in the brake disks and noise and vibration in the brake system. The critical sliding speed can be found by examining the conditions under which a perturbation in the temperature and stress fields can grow in time. The growth has exponential character, and subject to certain restrictions, the growth rate b is found to be real. The critical speed then corresponds to a condition at which b = 0 and hence at which there is a steady-state solution involuing nonuniform contact pressure. We first treat the heat sources Q at the contact nodes as given and use standard finite element analysis (FEA) to d...

On determining stress intensity factors for mixed mode cracks from thermoelastic data

Abstract: — An alternative methodology is presented for determining stress intensity factors for cracks subject to mixed-mode displacements. The methodology involves thermoelastic data generated from a SPATE (Stress Pattern Analysis by Thermal Emission) system and has been adapted from one used successfully in photoelasticity. The thermoelastic data is collected throughout the elastic stress field dominated by the crack tip singularity. The stress field is described using a Fourier series within Muskhelishvili's approach. This method allows different applied stress fields to be described which may include transient or non-uniform stress fields. The results obtained using the new methodology are at least as good as those obtained previously for pure mode I cases, and generally better for mixed mode displacement conditions.

Some direction-dependent properties of matrix-inclusion type composites with given reinforcement orientation distributions

Abstract: A Mori-Tanaka mean-field approach for predicting the overall thermoelastic properties of multi-phase composites with given orientation distributions of the inclusion phases is used to study the influence of the inclusion orientation distribution on the effective material properties. The aim of this study is primarily to understand the effects of the inclusion orientations in short-fiber-reinforced composites and to identify the basic mechanisms of interaction between the phases which govern the overall thermoelastic behavior. Perfectly aligned discontinuous fibers, various orientation distributions as well as two-dimensional and three-dimensional random orientations of the inclusions are studied. The overall Young's moduli, shear moduli and coefficients of thermal expansion, as well as the onset of yielding of the matrix phase under thermal and mechanical loading conditions, are calculated. The results are evaluated both in terms of the orientation distributions of the inclusions and in terms of the direction dependences of the predicted overall moduli. From these findings useful information on the appropriate requirements for the design of composite materials and composite structures can be obtained.

Optimization of Material Composition to Minimize Thermal Stresses in Nonhomogeneous Plate Subjected to Unsteady Heat Supply

Abstract: For a nonhomogeneous medium, both the heat conduction equation and the governing equations of an associated thermoelastic field are nonlinear in general. Therefore, theoretical treatment of these nonlinear equations is very difficult and an exact solution is almost impossible to obtain. By introducing a laminated composite model, we derived a one dimensional temperature solution for a nonhomogeneous plate in a transient state in our previous work. In the present work, making use of this temperature solution, we describe the optimization of material composition to minimize the transient thermal stress. As a numerical example, two nonhomogeneous plates, one composed of zirconium oxide/titanium alloy and the others of alumina/ aluminum alloy, are considered. Then the optimum material composition is determined by calculation. Furthermore, the temperaturedependence of material properties is discussed.

Thermoelastic stress analysis under nonadiabatic conditions

Abstract: Thermoelastic stress analysis is a full-field stress measurement technique complementary to local techniques like strain gages. Generally, the heat transfer inside the material is neglected with respect to the frequency of the cyclical loading. An adiabaticity criterion is established to assert this simplification as a function of the thermal diffusion length and the spatial stress gradients. Under nonadiabatic conditions, heat diffusion attenuates the spatial temperature gradients, which leads to an underestimation of stress concentrations. Analytical and numerical considerations allow for the quantification of the spatial resolution. Finally, several inverse techniques can restore the thermally attenuated contrasts.

Axisymmetric thermoelastic interactions without energy dissipation in an unbounded body with cylindrical cavity

Abstract: The linear theory of thermoelasticity without energy dissipation is employed to study thermoelastic interactions in a homogeneous and isotropic unbounded body containing a cylindrical cavity The interactions are supposed to be due to a constant step in radial stress or temperature applied to the boundary of the acvity, which is maintained at a constant temperature or zero radial stress (as the case may be) By using the Laplace transform technique, it is found that the interactions consist of two coupled waves both of which propagate with a finite speed but with no attenuation The discontinuities that occurs at the wavefronts are computed Numerical results applicable to a copper-like material are presented

A Variational Formulation, a Work-Energy Relation and Damping Mechanisms of Active Constrained Layer Treatments

Abstract: The purposes of this paper are to formulate active constrained layer (ACL) damping treatments through a variational approach, to study the work-energy relation of ACL, and to identify damping mechanisms of ACL treatments. Application of the extended Hamilton principle to ACL results in the equations of motion of ACL and the charge equation of electrostatics for the piezoelectric constraining layer. The work-energy equation together with the charge equation shows that the power dissipated through the active damping is the product of the electric field and the axial velocity of the piezoelectric constraining layer at the boundaries. This unique feature suggests that a set-sensing and actuating piezoelectric constraining layer may be an appropriate design in dissipating vibration energy without causing instability. To identify the damping mechanisms, a sensitivity analysis shows that the effectiveness ofA CL damping primarily depends on the active and passive damping forces transmitted to the vibrating structure through the viscoelastic layer. The active damping force transmitted depends on the controller transfer function as well as a system parameter, termed active damping sensitivity factor, which depends entirely on the configuration of the passive constrained layer and the sensor. Finally, numerical results on ACL beams are obtained to illustrate the theoretical predictions above.

Properties of Vibration with Fractional Derivative Damping of Order 1/2.

Abstract: The general properties of a harmonic oscillation with damping proportional to the fractional time derivative of the displacement of order 1/2 is studied. It is shown that vibration decays when the damping coefficient is positive, implying that the model is thermodynamically valid. The center of the oscillation is a curve that approaches the time axis algebraically, so that after the oscillation damps out, there is a long trailing tail. There is no critical value of the damping coefficient that distinguishes the pattern of damping. For a negative damping coefficient, oscillation grows exponentially. An equivalent oscillator model with ordinary damping may be constructed for small damping, which shows that fractional damping acts partly as a supplementary spring, reflecting the recoil effect of a viscoelastic material.

Thermoelastic stress analysis of a GRP tee joint

Abstract: A detailed study of the stresses that are developed in a glass reinforced plastic (GRP) tee joint under service loads is described. The joints are fabricated by laminating a boundary angle over a radiused fillet on either side of the ‘tee’. Full-field stress characterisation data is provided by a thermoelastic analysis of the tee joint. Calibration procedures that allow the thermoelastic data to be compared with the results of a finite element analysis are detailed. The results of the thermoelastic analysis are compared with values obtained from the finite element analysis. The applicability of thermoelastic analysis as a validation tool for finite element models of composite materials is assessed.

Generalization of Eshelby's Formula for a Single Ellipsoidal Elastic Inclusion to Poroelasticity and Thermoelasticity

Abstract: Eshelby{close_quote}s formula gives the response of a single ellipsoidal elastic inclusion in an elastic whole space to a uniform strain imposed at infinity. Using a linear combination of results from two simple thought experiments, we show how this formula may be generalized to both poroelasticity and thermoelasticity. The resulting new formulas are important for applications to analysis of poroelastic and thermoelastic composites, including but not restricted to rocks. {copyright} {ital 1997} {ital The American Physical Society}

FFT thermoelastic solutions for moving heat sources

Abstract: An analytical frequency domain solution is obtained using the spatial Fourier transform for thermal and thermoelastic fields due to an arbitrary heat source or thermal distribution moving at constant speed over the surface of an insulated, traction free elastic half space. Conversions between the space and frequency domains for the input and output are performed efficiently and robustly using FFT techniques. The method is validated by comparison to the analytical result for the moving line heat source in which it is shown that numerical evaluation of the analytical solution is problematic for large speeds or distances from the heat source. The utility of the method is illustrated on the constant patch moving heat source and discretely distributed multiple heat sources known as the hot spot problem. It is shown, through several examples, that the effect of hot spots on surface displacement and tangential stress is small. Finally, this conclusion is generalized by quantifying the frequency domain solution for the moving heat source problem as a low pass filter.

On Bonded Circular Inclusions in Plane Thermoelasticity

Abstract: A general solution to the thermoelastic problem of a circular inhomogeneity in an infinite matrix is provided. The thermal loadings considered in this note include a point heat source located either in the matrix or in the inclusion and a uniform heat flow applied at infinity. The proposed analysis is based upon the use of Laurent series expansion of the corresponding complex potentials and the method of analytical continuation. The general expressions of the temperature and stress functions are derived explicitly in both the inclusion and the surrounding matrix. Comparison is made with some special cases such as a circular hole under remote uniform heat flow and a circular disk under a point heat source, which shows that the results presented here are exact and general.