Effects of Thermomechanical Coupling and Relaxation Times on Wave Spectrum in Dynamic Theory of Generalized Thermoelasticity

1998 ◽  
Vol 65 (3) ◽  
pp. 605-613 ◽  
Author(s):  
C. S. Suh ◽  
C. P. Burger
Keyword(s):  
Relaxation Time ◽  
Wave Spectrum ◽  
Relaxation Times ◽  
Thermal Relaxation ◽  
Generalized Thermoelasticity ◽  
Thermomechanical Coupling ◽  
Order Of Magnitude ◽  
Relaxation Time Constants ◽  
Thermoelastic Waves ◽  
Insight Into

A spectral study is performed to gain insight into the effects of relaxation times and thermomechanical coupling on dynamic thermoe Iastic responses in generalized thermoelasticity. The hyperbolic thermoelastic theories of Lord and Schulman (LS) and Green and Lindsay (GL) are selected for the study. A generalized characteristic equation is derived to investigate dispersion behavior of thermoelastic waves as functions of thermomechanical coupling and relaxation time constants. Thermomechanical coupling is found to impose a significant influence on phase velocities. The GL model implicitly indicates that the order of magnitude of the thermomechanical relaxation time can never be greater than that of thermal relaxation time.

Thermal equilibration of samples for neutron scattering

2013 ◽  
Vol 46 (1) ◽  
pp. 279-285 ◽  
Author(s):  
Tobias K. Herman ◽  
Sarah C. Parks ◽  
Julia Scherschligt
Keyword(s):  
Relaxation Time ◽  
Neutron Scattering ◽  
Material Properties ◽  
Thermal Relaxation ◽  
Sample Cell ◽  
Time Constants ◽  
Thermal Equilibration ◽  
Temperature Relaxation ◽  
Relaxation Time Constants ◽  
Selection Of

Temperature relaxation and equilibration of samples for neutron scattering was investigated in a selection of samples and sample cells within the range of 5–300 K. A simple model was developed that relates thermal relaxation time constants to material properties of the sample and sample cell. This model should facilitate extension of this study to prediction of thermal behavior in other systems.

scholarly journals Rotation, Initial Stress, Gravity and Electromagnetic Field Effect on P Wave Reflection from Stress-Free Surface Elastic Half-Space with Voids under Three Thermoelastic Models

2020 ◽  
Vol 22 (1) ◽  
pp. 313-328 ◽  
Author(s):  
S. M. Abo-Dahab ◽  
S. Z. Rida ◽  
R. A. Mohamed ◽  
A. A. Kilany
Keyword(s):  
Free Surface ◽  
Gravity Field ◽  
Initial Stress ◽  
Complex Modulus ◽  
Plane Waves ◽  
Relaxation Times ◽  
Thermal Relaxation ◽  
Generalized Thermoelasticity ◽  
P Wave ◽  
Reflection Coefficients

AbstractThe present paper is devoted to investigate the influence of the rotation, thermal field, initial stress, gravity field, electromagnetic and voids on the reflection of P wave under three models of generalized thermoelasticity: Classical and Dynamical coupled model (CD), Lord-Shulman model (LS), Green-Lindsay model (GL), The boundary conditions at stress-free thermally insulated surface are satisfied to obtain Algebraic system of four equations in the reflection coefficients of various reflected waves. It is shown that there exist four plane waves; P1, P2, P3 and P4. In addition, the reflection coefficients from insulated and isothermal stress-free surface for the incident P wave are obtained. Finally, numerical values of the complex modulus of the reflection coefficients are visualized graphically to display the effects of the rotation, initial stress, gravity field magnetic field, thermal relaxation times and voids parameters.

scholarly journals On the flexural and extensional thermoelastic waves in orthotropic plates with two thermal relaxation times

2004 ◽  
Vol 2004 (1) ◽  
pp. 69-83 ◽  
Author(s):  
K. L. Verma ◽  
Norio Hasebe
Keyword(s):  
Orthotropic Plate ◽  
Finite Thickness ◽  
Relaxation Times ◽  
Thermal Relaxation ◽  
Orthotropic Plates ◽  
Special Cases ◽  
Thermal Relaxation Times ◽  
Modes Of Vibration ◽  
The Waves ◽  
Thermoelastic Waves

Analysis for the propagation of plane harmonic thermoelastic waves in an infinite homogeneous orthotropic plate of finite thickness in the generalized theory of thermoelasticity with two thermal relaxation times is studied. The frequency equations corresponding to the extensional (symmetric) and flexural (antisymmetric) thermoelastic modes of vibration are obtained and discussed. Special cases of the frequency equations are also discussed. Numerical solution of the frequency equations for orthotropic plate is carried out, and the dispersion curves for the first six modes are presented for a representative orthotropic plate. The three motions, namely, longitudinal, transverse, and thermal, of the medium are found dispersive and coupled with each other due to the thermal and anisotropic effects. The phase velocity of the waves gets modified due to the thermal and anisotropic effects and is also influenced by the thermal relaxation time. Relevant results of previous investigations are deduced as special cases.

scholarly journals On Propagation of Rayleigh Type Surface Wave in Five Different Theories of Thermoelasticity

2019 ◽  
Vol 24 (3) ◽  
pp. 661-673 ◽  
Author(s):  
B. Singh ◽  
S. Verma
Keyword(s):  
Relaxation Time ◽  
Surface Wave ◽  
Rayleigh Wave ◽  
Half Space ◽  
Wave Speed ◽  
Thermal Relaxation ◽  
Generalized Thermoelasticity ◽  
Governing Equations ◽  
Particular Solutions ◽  
Rayleigh Wave Speed

Abstract The governing equations for a homogeneous and isotropic thermoelastic medium are formulated in the context of coupled thermoelasticity, Lord and Shulman theory of generalized thermoelasticity with one relaxation time, Green and Lindsay theory of generalized thermoelasticity with two relaxation times, Green and Nagdhi theory of thermoelasticity without energy dissipation and Chandrasekharaiah and Tzou theory of thermoelasticity. These governing equations are solved to obtain general surface wave solutions. The particular solutions in a half-space are obtained with the help of appropriate radiation conditions. The two types of boundaries at athe surface of a half-space are considered namely, the stress free thermally insulated boundary and stress free isothermal boundary. The particular solutions obtained in a half-space satisfy the relevant boundary conditions at the free surface of the half-space and a frequency equation for the Rayleigh wave speed is obtained for both thermally insulated and isothermal cases. The non-dimensional Rayleigh wave speed is computed for aluminium metal to observe the effects of frequency, thermal relaxation time and different theories of thermoelasticity.

Electromagneto-Thermoelastic Plane Waves in Solids With Thermal Relaxation

1972 ◽  
Vol 39 (1) ◽  
pp. 108-113 ◽  
Author(s):  
A. H. Nayfeh ◽  
S. Nemat-Nasser
Keyword(s):  
Magnetic Field ◽  
Relaxation Time ◽  
Thermal Field ◽  
Plane Waves ◽  
Electric Displacement ◽  
Thermal Relaxation ◽  
Displacement Current ◽  
Perturbation Techniques ◽  
Thermoelastic Waves ◽  
The Magnetic Field

Perturbation techniques are used to study the influence of small thermoelastic and magnetoelastic couplings on the propagation of plane electromagneto-thermoelastic waves in an unbounded isotropic medium. The thermal relaxation time of heat conduction, and the electric displacement current are included in the analysis. It is found that the thermal field may affect transverse motions, and that the magnetic field may affect motions that occur parallel to its line of action.

Damping in thin circular viscothermoelastic plate resonators

2015 ◽  
Vol 93 (12) ◽  
pp. 1597-1605 ◽  
Author(s):  
D. Grover
Keyword(s):  
Circular Plate ◽  
Plate Theory ◽  
Relaxation Times ◽  
Thermal Relaxation ◽  
Thermomechanical Coupling ◽  
Transverse Motion ◽  
Mechanical Relaxation ◽  
Out Of Plane ◽  
Fixed Radius ◽  
Thermally Conducting

The governing equations of transverse motion and heat conduction of a homogenous, isotropic, thermally conducting, Kelvin–Voigt-type medium, based on Kirchhoff–Love plate theory, are established for out-of-plane vibrations of a generalized viscothermoelastic circular thin plate. The analytical expressions for thermoelastic damping of vibration and frequency shift are obtained for generalized and coupled viscothermoelastic plates. It is noticed that the damping of vibrations significantly depends on mechanical relaxation times and thermal relaxation time in addition to thermomechanical coupling in a circular plate under resonance conditions. The surface conditions also impose significant effects on the vibrations of such resonators. The numerical results may also be illustrated in the case of a circular plate and an axisymmetric circular plate for clamped and simply supported boundary conditions for fixed aspect ratio, fixed radius, and fixed thickness, respectively.

Relations Between Pore Size Fluid and Matrix Properties, and NML Measurements

1970 ◽  
Vol 10 (03) ◽  
pp. 268-278 ◽  
Author(s):  
J.D. Loren ◽  
J.D. Robinson
Keyword(s):  
Relaxation Time ◽  
Pore Size ◽  
Pore Space ◽  
Laboratory Data ◽  
Thermal Relaxation ◽  
Residual Oil ◽  
Mercury Injection ◽  
Order Of Magnitude ◽  
Water Response ◽  
Mercury Injection Capillary Pressure

Abstract A theory relating proton relaxation times for water and hydrocarbons confined to rock pores to the pore size distribution of rocks and providing the basis for Nuclear Magnetism Log (NML) interpretation is presented. A model proposed by Senturia and Robinson relates the thermal relaxation time (T1) of the proton spins of molecules in the liquid state to proton spins of molecules in the liquid state to geometrical and physical properties of a liquid-filled porous solid. Four parameters enter their theory, namely, jump distance and correlation time of the liquid molecules, radius of the confining region a, and the probability (1-p) for proton spin-flip at the liquid-solid interface. In this report the theoretical model of Ref. 1 is used to analyze thermal relaxation measurements on a suite of liquid-saturated porcelain samples. The assumption that pore size is inversely proportional to mercury injection capillary pressure proportional to mercury injection capillary pressure (Pc) enables the T1 of the liquid-saturated porous solid to be expressed as where l/r is the thermal relaxation time of the bulk liquid, and is a parameter containing, p and a constant of proportionality. The suite of porcelain samples have mercury injection displacement pressures ranging from 20 to 200 psi; yet values of pressures ranging from 20 to 200 psi; yet values of derived from the measured values of T1, r and Pc are relatively constant as predicted by the theory. When the identical porcelain samples are saturated with decane rather than water, there is an order of magnitude decrease in; this leads to the conclusion that the T1 of a water-wet, hydrocarbon-saturated rock is relatively insensitive to pore size. Values of determined for a suite of water-saturated sandstones with widely varying pore sizes range from 0.13 psi-1 sec-1 to 0.44 psi-1 sec-1. Measurements on samples with both a water and an oil phase present illustrate the insensitivity of the T1 of the oil phase to the geometry of the confining pore space. pore space. Within carbonates, the observed value of is an order of magnitude less than in sands. This reduction could be brought about by either a change in the factor of proportionality relating pore size to pore entry size, or by a decrease in the probability for relaxation at the surface. Within rocks containing both water and oil, the known values of and the assumption that the oil phase occupies the larger pores permits thermal phase occupies the larger pores permits thermal relaxation curves to be calculated which fit observed data. A method for quantitatively determining residual oil involves use of a paramagnetic aqueous phase to effectively kill the water response and phase to effectively kill the water response and permit the remaining signal to be attributed to the permit the remaining signal to be attributed to the oil phase. This theory provides the basis for NML interpretation. For example, application of the theory permits a pore size histogram to be determined from permits a pore size histogram to be determined from a thermal relaxation curve derived histogram is dependent upon the uncertainty associated with each point on the thermal relation curve; and the fraction of the total proton magnetization observed. Another application is the quantitative determination of residual oil from down-hole thermal relaxation data. Introduction The signal recorded on an NML is obtained directly from fluids contained in the pores of a rock. A proper understanding of the relation between the observed response and matrix and fluid properties is essential for the interpretation of the log. In this report, a physical model is presented which provides this relation. Laboratory data from provides this relation. Laboratory data from porcelain and natural cores containing both water and porcelain and natural cores containing both water and hydrocarbon are analyzed in terms of the model. SPEJ p. 268

scholarly journals Revisiting the thermal relaxation of neutron stars

2020 ◽  
Vol 642 ◽  
pp. A42
Author(s):  
Thiago Sales ◽  
Odilon Lourenço ◽  
Mariana Dutra ◽  
Rodrigo Negreiros
Keyword(s):  
Relaxation Time ◽  
Surface Temperature ◽  
Neutron Stars ◽  
Equations Of State ◽  
Thermal Evolution ◽  
Relaxation Times ◽  
Thermal Relaxation ◽  
Neutrino Production ◽  
Fast Cooling ◽  
Late Relaxation Time

In this work, we revisit the thermal relaxation process for neutron stars. Such a process is associated with the thermal coupling between the core and the crust of neutron stars. The thermal relaxation, which takes place at around 10–100 years, is manifested as a sudden drop in the star’s surface temperature. Such a drop is smooth for slowly cooling objects and very sharp for fast-cooling ones. In our study, we focused particularly on the cooling of neutron stars whose mass is slightly greater than the value above which the direct Urca (DU) process sets in. Considering different mechanisms for neutrino production in each region of the star, and working with equations of state with different properties, we solved the thermal evolution equation and calculated the thermal relaxation time for an ample range of neutron star masses. By performing a comprehensive study of neutron stars just above the onset of the DU process, we show that stars under these conditions exhibit a peculiar thermal relaxation behavior. We demonstrate that such stars exhibit an abnormally late relaxation time, characterized by a second drop in its surface temperature taking place a later age. We qualified such behavior by showing that it is associated with limited spatial distribution of the DU process in such stars. We show that as the star’s mass increases, the DU region also grows, and the star exhibits the expected behavior of fast-cooling stars. Finally, we show that one can expect high relaxation times for stars in which the DU process takes place in a radius no larger than 3 km.

The Effect of Relaxation Times on Thermoelastic Damping in a Nanobeam Resonator

2016 ◽  
Vol 04 (02) ◽  
pp. 1650001 ◽  
Author(s):  
Ibrahim A. Abbas
Keyword(s):  
Relaxation Time ◽  
Present Model ◽  
Relaxation Times ◽  
Thermal Relaxation ◽  
Beam Deflection ◽  
Thermoelastic Damping ◽  
Coupled Thermoelasticity ◽  
Special Cases ◽  
Thermal Relaxation Times ◽  
Gl Theory

In the present work, in accordance with the generalized theory of thermoelasticity with two thermal relaxation times, the vibration of a thick finite nanobeam resonator has been considered. Both the general thermoelasticity and coupled thermoelasticity (CT) theories with only one relaxation time can be deduced from the present model as special cases. Under clamped conditions for beam, the effect of relaxation times in nanobeam resonator has been investigated. Based on the analytical relationships, the beam deflection, temperature change, frequency shift and thermoelastic damping were investigated and the numerical results were graphically obtained. According to the observed results there is a clear difference between the CT theory, Lord and Shulman’s (LS) theory and Green and Lindsay’s (GL) theory.

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