Showing papers on "Thermoelastic damping published in 1974"

Dynamic behaviour of structures with embedded foundations

Abstract: A study of the dynamics of building-soil interaction is presented that includes embedding of the foundation and material damping. By considering buildings on rigid footings embedded into linear elastic soil with hysteretic damping, it is shown that the earthquake response of the building-foundation model may be found from the response to modified excitation of equivalent one-degree-of-freedom linear, viscously damped oscillators resting on rigid ground. For a single-storey building approximate formulas are developed for the modified natural frequency and damping ratio. Results show that the natural frequency and damping in the system increase with embedding. Effective damping also increases with internal friction in the soil. Ignoring these two factors may underestimate considerably the effective natural frequency and damping in the system. In spite of additional sources of energy dissipation provided by the soil, damping in the equivalent oscillator may be greater or smaller than that corresponding to the superstructure alone, depending upon the system parameters. For lightly damped superstructures, the peak amplitude of the steady-state overturning moment at the base of a building supported on flexible soil is significantly smaller than that corresponding to rigid ground. This result has practical implications for earthquake design.

Morphology and Crystallography of Thermoelastic Cu–Al–Ni Martensite Analyzed by the Phenomenological Theory

Abstract: The thermoelastic martensite transformation from theβ1 phase to the γ' phase in Cu-Al-Ni alloy has been analyzed by the phenomenological theory, special attention being given to the understanding of the unique morphology. It is shown that there are a pretty good agreement between the theory and experiment with respect to the habit plane and the orientationrelationship and a less good agreement with respect to the relative twin width,for δ=1. The unique \"spear-like\" mor-

Thermo-mechanics of rubberlike materials

Abstract: A theoretical study is made in this paper of the formulation of constitutive equations describing the thermo-mechanical response of solid polymers in the temperature range in which they exhibit rubberlike behaviour. An expression for the Helmholtz free energy of such a material is first constructed on the basis of two assumptions which are motivated by physical arguments concerning the relation of the molecular structure of a cross-linked polymer to its bulk response. The constitutive equations for the stress and the entropy generated by the proposed form of the free energy function are then employed m a detailed investigation of the extension of a cylindrical specimen under prescribed conditions of temperature and pressure, a situation which serves as a model of the experimental arrangement most frequently used in laboratory studies of the mechanical and thermo-mechanical properties of rubberlike solids. Qualitative consistency of the theoretical predictions with observed behaviour is shown to be assured, over the full range of circumstances for which measurements have been reported, by two simple inequalities affecting one of the three response functions appearing in the stress-deformation-temperature relations. The function concerned is closely related to the strain energy governing isothermal deformations of the material at a selected reference temperature and it is associated, by the physical considerations referred to above, with the contribution to the stress of the polymer network. This conclusion shows that a rational macroscopic theory of rubberlike thermoelasticity can be developed in rather general terms. In particular, the requirement that the constitutive equations shall reproduce the anomalous thermo-mechanical effects which are characteristic of solid elastomers imposes restrictions on the response functions no more severe than those which ensure that the purely mechanical behaviour of the material is physically realistic. In the remainder of the paper the capability of the basic theory for furnishing results quantitatively agreeing with experiment is examined. Empirical forms of the three response functions are presented which accurately represent measurements made in tests involving compression at different fixed temperatures and stretching at the reference temperature. Numerical calculations relating to the analysis of the extension of a cylinder, given earlier, are then described and compared with the results of experiments in which thermoelastic inversion phenomena occur. Satisfactory agreement is secured, but it is noted that insufficiency of material data for the rubbers used in the tests precludes an exact correlation of theory and experiment. The final section of the paper is concerned with isothermal deformations of rubberlike materials which are mechanically incompressible (in the sense that volume changes can be brought about by thermal expansion but not by loading at fixed temperature). This property closely approximates the typical behaviour of natural and synthetic rubbers, but its incorporation into a general treatment of rubberlike thermoelasticity presents difficulties and places an undesirable limitation on the scope of the theory. An analogue is shown to exist between the constitutive equations for deformations at the reference temperature and their counterparts in respect of isothermal deformations at other temperatures, and with its aid the problem of the combined extension, torsion and uniform heating of a circular cylinder is solved. Again, a numerical evaluation of the solution is compared with available experimental data.

A Thermal, Thermoelastic, and Wear Simulation of a High-Energy Sliding Contact Problem

Abstract: This paper describes an investigation of the sliding contact problem encountered in high-energy disk brakes. The analysis includes a simulation modeling, using the finite element method, of the thermoelastic instabilities that cause transient changes in contact to occur on the friction surface. In order to include the effect of wear of the concentrated contacts on the friction surface, a wear criterion is proposed that results in prediction of wear rates for disk brakes that are quite close to experimentally determined wear rates. The thermal analysis shows that the transient temperature distribution in a disk brake can be determined more accurately by use of this thermomechanical analysis than by a more conventional analysis that assumes constant contact conditions. It is also shown that lower, more desirable, temperatures in disk brakes can be attained by increasing the volume, the thermal conductivity, and especially, the heat capacity of the brake components.

Reflection of thermoelastic waves at a solid half-space with thermal relaxation

Abstract: The thermal and elastic plane wave motion of small amplitude in a homogeneous, isotropic and thermally conducting solid which occupies a half-space is considered. The presence of the thermal waves effect change in the angle of emergence.

Thermoelastic waves in anisotropic solids

Abstract: As motivated by the recent discovery of heat pulses propagating in dielectric crystals at low temperature, a continuum theory of thermoelasticity, which is modified to include the effect of thermal phonon relaxation, is applied to investigate the propagation of plane harmonic waves in unbounded anisotropic solids Four characteristic wave speeds are found, three being analogous to those of isothermal or adiabatic elastic waves The fourth wave, which is predominantly a temperature disturbance, corresponds to the heat pulses known also as the second sound Velocity, slowness, and wave surfaces of the thermoelastic waves are analyzed and are illustrated with numerical and graphical results for NaF and solid helium crystals A new definition of the group velocity for waves in a dissipative and dispersive anisotropic medium is proposed and is calculated and compared with the energy transport speed of thermoelastic waves

Laminate having a compressed foam core

Abstract: Laminates comprising two cover layers and a core of a thermoelastic foam, such as of a polymethacrylimide resin, said foam being compressed while in a thermoelastic condition and cooled below the softening point while maintaining compressive pressure thereon. The core is arranged in the laminate so that the compression direction is parallel to the plane of the cover layers, since maximum strength properties are developed in the compressed foam in directions perpendicular to the compression direction.

Oscillatory shearing of nonlinearly elastic solids

Abstract: A finite oscillatory shearing motion is shown to be possible, in the absence of body force, in every homogeneous isotropic compressible or incompressible elastic solid. The spatial geometry is the same for all materials and the nature of the time-dependence, for a particular material, is determined by the generalized shear modulus. A motion of this type and a spatially uniform, time-dependent temperature can be supported in thermoelastic solids, without application of body force or volume supply of heat.

The thermoelastic effect in PMMA

Abstract: The thermoelastic effect has been measured in polymethylmethacrylate under both tensile and compressive uniaxial stress and the resulting temperature change for a known applied stress has been used to calculate the linear expansion coefficient of PMMA over a range of temperatures from 295 to 355 K and uniaxial stress in the elastic range using the Thompson relationship: Δθ= − αTΔσ/ρCp.

Thermoelastic constitutive equations for chemically hardening materials

Abstract: Thermoelastic constitutive equations are derived for a material undergoing solidification or hardening as the result of a chemical reaction. The derivation is based upon a two component model whose composition is determined by the degree of hardening, and makes use of strain-energy considerations. Constitutive equations take the form of stress rate-strain rate relations, in which the coefficients are time-dependent functions of the composition. Specific results are developed for the case of a material of constant bulk modulus which undergoes a transition from an initial liquidlike state into an isotropic elastic solid. Potential applications are discussed.

On the theory of thermoelastic bending of reinforced shells and plates

Abstract: The author examines an approach to the construction of a theory of thermoelastic bending of arbitrarily reinforced shells and plates that takes into account the actual structure, the deformation characteristic, and the actual thermomechanical properties of the elements which make up the composite. The final equations are obtained with and without allowance for transverse shear strains. The problem of the thermoelastic bending of a thin, arbitrarily reinforced rectangular plate hinged at the edges, when transverse shear strains can be neglected, is considered as an example.

Ni(NO3)2.6NH3, another example of KCN-type anomalous thermoelastic behaviour

Abstract: The temperature dependence of all elastic constants of cubic Ni(NO3)2.6NH3, measured from the transition point at - 34.2 to 150°C by ultrasonic methods, exhibits KCN-type anomalous behaviour. Within a wide temperature range all elastic wave velocities increase with higher temperature. The shear resistance c” = (c11 - c12)/2 corresponds to the constant c44 in KCN. The change of c” with absolute temperature obeys a logarithmic law like c44 in KCN, namely c” = a log T/T0 with a = 0.05975 . 1011 dyn cm-2 and T0 = 156.22°K. The anomalous elastic behaviour should be assigned mainly to the thermally activated motions of the NO3 ions. The phase transition is directly related to the low c” value.

Elastic and thermal expansion anisotropy of oriented linear polyethylene

Abstract: A two-phase composite laminate model is proposed for representing biaxially oriented sheets of linear polyethylene. Thermoelastic analysis of the model yields predictions of the complete elastic and thermal expansion anisotropy. These predictions are compared with experimental measurements of elastic compliance and thermal expansivity obtained with the same oriented sheets. Using only one adjustable parameter (Poisson's ratio of non-crystalline linear polyethylene), extensive qualitative agreement is obtained between model predictions and experimental results. Discrepancies which are observed are attributed to the influence of the interfacial regions which exist between adjacent stacks of lamellar crystals in the real oriented sheets.

Thermoelastic Properties of Unidirectional Filamentary Composites by a Semiempirical Micromechanics Theory

Abstract: : A unified, semiempirical micromechanics theory is described which relates the thermoelastic properties of the unidirectional, filamentary composite to the quantities and to the corresponding properties of its constituent materials. The theory treats the composite, the filaments and the matrix as being generally orthotropic, linearly elastic, and accounts for the effect of voids. It is based on the equivalent section concept, on parallel and series connected elements and on the judicious incorporation of certain empirical factors, which reflect the particular fabrication process. Results are presented which demonstrate and verify application of this theory to boron, carbon and glass-filament epoxy-resin composites. Additional results are presented which exhibit the voids and in-situ matrix orthotropicity effects on the thermoelastic properties of the unidirectional composite. Finally, results are included for all the thermoelastic properties of boron, carbon and glass-filament epoxy-resin composites. (Author)

Thermoelastic articles and process of manufacture thereof

Abstract: A process is described and the product thereof, for the manufacture of a thermoelastic product wherein a blend of a vulcanizable crystalline elastomer, a crystalline wax and a vulcanizing agent are vulcanized The thermoelastic product has the property of being able to store elastic stresses imposed on it and of being able to release these stresses when warmed slightly

The effect of coulomb damping on multidegree of freedom elastic structures

Abstract: This paper is based on the premise that the damping mechanism of a multidegree of freedom structure can be represented by viscous and coulomb dampers. A closed form solution for the structure subjected to a sinusoidal forcing function is presented. The solution is used as the basis of a method for determining relative amounts of viscous and coulomb damping from vibration tests. The method was applied to the results of a series of vibration tests on a five storey reinforced concrete structure and approximate values of viscous and coulomb damping obtained. A comparison of the effect of various combined damping values on the earthquake response of the structure was made. It was concluded that the use of the equivalent viscous damping concept to approximate the combined effect of viscous and coulomb damping results in a low estimate of the elastic response of the structure.

On the use of incomplete constitutive information in thermoelasticity

Abstract: The extent to which non-linear thermoelastic constitutive data may be determined by controllable states is delineated, and thermomechanical states that may be analyzed completely with such incomplete data are catalogued. These include non-homogeneous finite deformations coupled with quite general temperature fields in plane, cylindrical and spherical geometries. Two problems involving the states are worked out as examples.