Showing papers on "Thermoelastic damping published in 1993"

Thermoelasticity without energy dissipation

Abstract: This paper deals with thermoelastic material behavior without energy dissipation; it deals with both nonlinear and linear theories, although emphasis is placed on the latter. In particular, the linearized theory of thermoelasticity discussed possesses the following properties: (a) the heat flow, in contrast to that in classical thermoelasticity characterized by the Fourier law, does not involve energy dissipation; (b) a constitutive equation for an entropy flux vector is determined by the same potential function which also determines the stress; and (c) it permits the transmission of heat as thermal waves at finite speed. Also, a general uniqueness theorem is proved which is appropriate for linear thermoelasticity without energy dissipation.

A continuum model of a thermoelastic solid capable of undergoing phase transitions

Abstract: We construct explicitly a Helmholtz free energy, a kinetic relation and a nucleation criterion for a one-dimensional thermoelastic solid, capable of undergoing either mechanically- or thermally-induced phase transitions. We study the hysteretic macroscopic response predicted by this model in the case of quasistatic processes involving stress cycling at constant temperature, thermal cycling at constant stress, or a combination of mechanical and thermal loading that gives rise to the shape-memory effect. These predictions are compared qualitatively with experimental results.

Low‐frequency dispersion and attenuation in partially saturated rocks

Abstract: A theory is developed for the attenuation and dispersion of compressional waves in inhomogeneous fluid‐saturated materials. These effects are caused by material inhomogeneity on length scales of the order of centimeters and may be most significant at seismic wave frequencies, i.e., on the order of 100 Hz. The micromechanism involves diffusion of pore fluid between different regions, and is most effective in a partially saturated medium in which liquid can diffuse into regions occupied by gas. The local fluid flow effects can be replaced on the macroscopic scale by an effective viscoelastic medium, and the form of the viscoelastic creep function is illustrated for a compressional wave propagating normal to a layered medium. The wave speeds in the low‐ and high‐frequency limits are associated with conditions of uniform pressure and of uniform ‘‘no‐flow,’’ respectively. These correspond to the isothermal and isentropic wave speeds in a disordered thermoelastic medium.

Mechanism of the As temperature increase by pre-deformation in thermoelastic alloys

Abstract: The Ti-Ni-Nb shape memory alloys are attracting recent attention for the wide transformation temperature hysteresis, whih is caused by the A s increase due to pre-deformation, since it is suitable for pipe couplings. To find out the origin for the A s increase by pre-deformation, similar investigation was made by tensile tests, electrical resistance measurements, optical microscopy and transmission electron microscopy (TEM), for a Cu-13.8%Al-4.0%Ni (mass%) single cyrstal and Ti-50%Ni and Ti-50.5%Ni(at%) polycrystals, which exhibit the thermoelastic martensitic transformation

Frictionally Excited Thermoelastic Instability in Automotive Drum Brakes

Abstract: Thermoelastic instability in automotive drum brake systems is investigated using a finite layer model with one-sided frictional heating. With realistic material properties of automotive brakes, the stability behavior of the one-sided heating mode is similar to that of the antisymmetric mode of two-sided heating but the critical speed of the former is higher than that of the latter. The effects of the friction coefficient and brake material properties on the critical speeds are examined and the most influential properties are found to be the coefficient of friction and the thermal expansion coefficient of drum materials. Vehicle tests were performed to observe the critical speeds of the drum brake systems with aluminum drum materials. Direct comparisons are made between the calculation and measurement for the critical speed and hot spot spacing. Good agreement is achieved when the critical speeds are calculated using the temperature-dependent friction material properties and the reduced coefficient of friction to account for the effect of intermittent contact.

Generalized thermoelasticity: closed-form solutions

Abstract: A study of the one-dimensional thermoelastic waves produced by an instantaneous plane source of heat in homogeneous isotropic infinite and semi-infinite bodies of the Green-Lindsay (G-L) type is presented. Closed-form Green's functions corresponding to the plane heat source are obtained using the decomposition theorem for a potential-temperature wave of the G-L theory. Qualitative analysis of the results is included.

Vibration damping of large structures induced by attached small resonant structures

Abstract: The paper presents a simple deterministic derivation of the vibration damping induced in a large main structure by a multitude of small substructures attached more‐or‐less compliantly to the main structure, each dissipating vibratory power at its frequencies of resonance. A simple expression is obtained for the damping induced in the large structure indicating that the damping depends primarily on the total effective mass of substructures resonating within a band centered at the frequency of vibration, and is relatively independent of the damping factors of the individual substructures. The application of this simple expression for induced damping is illustrated by calculating the damping induced by substructures attached to an axially vibrating rod and to a flexurally vibrating beam. For the latter case, the calculated damping factors are compared with measured values.

Dynamic Analysis and Design of Laminated Composite Beams with Multiple Damping Layers

Abstract: This paper describes the formulation of a theory for the prediction of damping and natural frequencies of laminated composite beams with multiple viscoelastic damping layers. The damping layers are constrained (or sandwiched) by anisotropic laminates. The in-plane shear strains of the damping layers and the constraining layers are included in the model. Closed-form solutions for the resonance frequencies and modal loss factors of the composite beam system under simple supports are derived using the energy and Ritz method. A parametric study has been conducted to study the variation of dynamic stiffness and modal loss factor of the system with structural parameters (e.g., the ply orientations of laminas, thickness of the damping layers and the laminates), operating temperature, and damping material properties. The design of composite beams for maximizing the damping capacity is also presented in this paper which includes the determination of operating temperature range corresponding to given structural parameters and finding optimal structural parameters corresponding to given temperature range. Finally, some experimental results are compared with theory for the cases of single and double damping layer beam systems that show good agreement between predicted and measured natural frequencies.

Thermomechanical response of shape memory composites

Abstract: The Mori-Tanaka micromechanics method is used to predict the effective properties of composite materials consisting of a polymer matrix reinforced by a fiber made of a transformation shape memory effect (SME) material. The composite response is plotted for combinations of the following scenarios: (1) isothermal longitudinal and transverse stress input, (2) stress-free thermal loading, (3) constant fiber thermoelastic properties, and (4) thermoelastic fiber properties that vary with the martensite volume fraction. For the case of an isothermal stress input, the composite transformation stress, the maximum transformation strain, and the hysteresis are all reduced vis-a-vis the monolithic SME material. In contrast to a monolithic SME material, stress-free thermal loading of a SME composite can produce a transformation strain. It is shown that closed form solutions for the effective martensite and austenite start temperatures can be derived, that they are sensitive to the stress-free reference temperature of the fiber, and that the stress-free austenite and martensite start temperatures are higher than those of the monolithic SME material.

Modelling of dynamic networks of thin thermoelastic beams

Abstract: We derive a distributed-parameter model of a thin non-linear thermoelastic beam in three dimensions. The beam can also be initially curved and twisted. Our main task is to formulate the non-homogeneous initial, boundary and node value problem associated with the dynamics of a network of a finite number of such beams. The emphasis here is on a distributed-parameter modelling of the geometric and kinematic node conditions. The forces and couples appearing in the boundary and node conditions can then be viewed as control variables. The analysis of the resulting control systems and their controllability and stabilizability properties is the subject of [25] and of forthcoming papers.

Viscoelastic Mechanical Damping Devices Tested at Real Earthquake Displacements

Abstract: Experimental steady‐state hysteretic characteristics of ten direct shear seismic damping devices (DSSDs) are presented The devices were tested over a range of frequencies and displacements chosen as representative of building responses during moderate to severe level earthquakes Three different damping materials, produced by 3M Corporation and Lord Corporation, were used in the devices Excitation frequency, strain amplitude, damping material initial temperature, temperature change over the test duration, cyclic energy dissipation, and damping material moduli (including complex shear, storage and loss moduli) are reported for all tests performed The influence of frequency, displacement amplitude, temperature, and cumulative energy absorption on the damping material mechanical properties and hysteretic stability are examined Methods by which material moduli can be used to design damping devices for specified spring stiffness and equivalent viscous damping are presented Limitations of the hyst

Exponential stability of the semigroup associated with a thermoelastic system

Abstract: In this paper it is proved that the semigroup associated with the onedimensional thermoelastic system with Dirichlet boundary conditions is an exponen12 2 tially stable C0-semigroup of contraction on the space H0 x L x L . The technique of the proof is completely different from the usual energy method. It is shown that the exponential decay in 3 (s/) recently obtained by Revira is a consequence of our main result. An important application of our main result to the Linear-QuadraticGaussian optimal control problem is also discussed.

Residual Stresses in Fiber‐Reinforced Ceramics due to Thermal Expansion Mismatch

Abstract: Principles for the calculation of residual stresses due to thermal expansion mismatch and previous solutions are reviewed. A general model for this subject is proposed. Considering the effective thermoelastic properties of a unidirectional composite in axial and transverse directions allows a more comprehensive treatment of the residual stress situation in fiber-reinforced composites. Parameter variations show the important influence of the thermomechanical properties of an interfacial layer, which is disregarded in most of the conventional calculations.

Thermoelastic contact with Barber's heat exchange condition

Abstract: We consider a nonlinear parabolic problem that models the evolution of a one-dimensional thermoelastic system that may come into contact with a rigid obstacle. The mathematical problem is reduced to solving a nonlocal heat equation with a nonlinear and nonlocal boundary condition. This boundary condition contains a heat-exchange coefficient that depends on the pressure when there is contact with the obstacle and on the size of the gap when there is no contact. We model the heat-exchange coefficient as both a single-valued function and as a measurable selection from a maximal monotone graph. Both of these models represent modified versions of so-called imperfect contact conditions found in the work of Barber. We show that strong solutions exist when the coefficient is taken to be a continuously differentiable function and that weak solutions exist when the coefficient is taken to be a measurable selection from a maximal monotone graph. The proofs of these results reveal an interesting interplay between the regularity of the initial condition and the behavior of the coefficient at infinity.

The Influence of Cool-Down Temperature Histories on the Residual Stresses in Fibrous Metal-Matrix Composites

Abstract: The vanishing fiber diameter model together with the thermoviscoplastic ity theory based on overstress including a recovery of state formulation is introduced. They are employed to analyze the effects of temperature rate and of annealing at constant temperature on the residual stresses at room temperature when unidirectional fibrous metal-matrix composites are cooled down from 1000°C during the manufacturing process. For the present analysis the fibers are assumed to be transversely isotropic thermoelastic and the matrix constitutive equation is isotropic thermoviscoplastic including recovery of state. All material functions and constants can depend on current temperature. Yield sur faces and loading/unloading conditions are not used in the theory in which the inelastic strain rate is solely a function of the overstress, the difference between stress and the equi librium stress, a state variable of the theory. Assumed but realistic material elastic and vis coplastic properties as a function of temperature...

Thermoelastic Damping of a Laminated Beam in Flexure and Extension

Abstract: In a classic paper, Clarence Zener [1] considered transverse vibrations of an isotropic, homogenous, thermoelastic beam. He observed that the tensile side of such a vibrating beam cools while the compressional side heats up, resulting in irreversible heat transfer. This observation led him to predict the existence of thermoelastic damping. Pas sive damping is a critically important property from the viewpoint of vibration suppres sion in large, flexible space structures. Unfortunately, Zener's model cannot be extended to calculate damping in heterogeneous materials; therefore, in this article a more funda mental approach is taken. The Second Law of Thermodynamics is taken as the starting point, and the thermoelastic damping is calculated from the entropy created by the irre versible heat transfer in the medium. As a first step toward constructing a general theory for thermoelastic damping in composite materials, we solve the problem of a three-layer beam subjected to uniaxial tension and pure flexure.

Wave-drift damping of floating bodies

Abstract: Wave-drift damping results from low-frequency, oscillatory- motions of a floating body, in the presence of an incident wave field. Previous works have analysed this effect in a quasi-steady manner, based on the rate of change of the added resistance in waves, with respect to a small steady forward velocity. In this paper the wave-drift damping coefficient is derived more directly, from a perturbation analysis where the low-frequency body oscillations are superposed on the diffraction field. Unlike the case of body oscillations in calm water, where the damping due to wave radiation is asymptotically small for low frequencies, the superposition of oscillatory motions on the diffraction field results in an order-one damping coefficient. All three degrees of freedom are considered in the horizontal plane. The resulting matrix of damping coefficients is derived from pressure integration on the body, and transformed in special cases to a far-field control surface.

Thermoelastic interactions in an unbounded body with a spherical cavity

Abstract: Thermoelastic interactions caused in a homogeneous and isotropic unbounded body with a spherical cavity due to harmonically varying thermal field applied to the stress-free boundary of the cavity are considered. A unified system of governing equations that includes among its particular cases the field equations of the conventional as well as generalized thermoelasticity theories is employed. Closed form expressions for the temperature, displacement, and stress fields are obtained. Numerical results for a steel material are presented.

A one-dimensional quasi-static contact problem in linear thermoelasticity

Abstract: The existence, uniqueness and regularity of the solution to a one-dimensional linear thermoelastic problem with unilateral contact of the Signorini type are established. A finite element approximation is described, and an error bound is derived. It is shown that if the time step is O(h2), then the error in L2 in the temperature and in L∞ in the displacement is O(h). Some numerical experiments are presented.