scholarly journals The influence of the static-pre-stress and mechanical damage variable in the thermal quality factor of two-temperature viscothermoelastic resonators

2020 ◽  
Vol 12 (6) ◽  
pp. 168781402093045 ◽  
Author(s):  
Hamdy M Youssef ◽  
Mohammed W Al-Hazmi
Keyword(s):  
Relaxation Time ◽  
Quality Factor ◽  
Relaxation Times ◽  
Thermal Relaxation ◽  
Mechanical Damage ◽  
Damage Variable ◽  
Mechanical Relaxation ◽  
Length Scale ◽  
Quality Factors ◽  
Two Temperature

The mechanical damage variable, as well as the thermal and mechanical relaxation times, plays essential roles in the thermal quality factor of the resonators, where controls energy damping through the coupling of mechanical and thermal behavior. In this article, we developed a mathematical model in which a static-pre-stress and mechanical damage variable in the context of a two-temperature viscothermoelasticity of silicon resonator has been considered. The effects of static-pre-stress, thermal relaxation time, mechanical relaxation time, mechanical damage variable, isothermal frequency, and length-scale on the quality factor have been discussed in the context of a one-temperature and two-temperature models. The model predicts that significant improvement in terms of quality factors is possible by tuning the static-pre-stress, isothermal frequency, and length-scale of the resonator. Moreover, the thermal and mechanical relaxation times and the mechanical damage variable have impacts on the thermal quality factor.

scholarly journals Influence of the Static Pre-Stress in Micro-Viscothermoelastic Resonators Based on Dual-Phase-Lagging Heat Conduction

2020 ◽  
Vol 2020 ◽  
pp. 1-8
Author(s):  
Najat A. Alghamdi ◽  
Hamdy M. Youssef
Keyword(s):  
Heat Conduction ◽  
Energy Dissipation ◽  
Thermal Behavior ◽  
Quality Factor ◽  
Analytical Model ◽  
Relaxation Times ◽  
Mechanical Relaxation ◽  
Length Scale ◽  
Dual Phase ◽  
Quality Factors

Thermal and mechanical relaxation times play vital roles in the values of the quality factor of micro/nanoresonators. They can control the energy dissipation across the coupling of mechanical and thermal behavior. In this paper, we introduce an analytical model that considers a pre-stress in a micro-viscothermoelastic resonator to modify the thermal and mechanical relaxation times and thus higher the quality factor. The impacts of length scale and static pre-stress on the quality factor have been discussed. The model expects that significant improvement in terms of quality factors is possible by tuning the pre-stress and the thermal and mechanical relaxation times parameters, and the isothermal value of frequency have significant effects on the thermal quality factor of the resonators.

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.

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.

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.

THERMAL RELAXATION TIMES OF BISTABLE THIN FILM ELEMENTS

1993 ◽  
Vol 02 (02) ◽  
pp. 209-220 ◽  
Author(s):  
V. GLAW ◽  
K. JANIAK ◽  
A. KUMMROW ◽  
V. PENSCHKE ◽  
H.J. EICHLER
Keyword(s):  
Thin Film ◽  
Heat Capacity ◽  
Relaxation Time ◽  
Optical Bistability ◽  
Relaxation Times ◽  
Thermal Relaxation ◽  
Interference Filters ◽  
Spot Radius ◽  
Thermal Relaxation Times ◽  
Thin Film Interference

The heat flow in evaporated thin film interference filters with CdS spacer and an optional CdSe absorption layer is investigated, analyzing the dynamics of optical bistability. The influence of the spot radius r of the exciting laser beam on the switching parameters is studied experimentally and theoretically. The response to pulsed excitation of the bistable devices can be described with a relaxation time τ~r and an effective nonlinearity χ~r−2 which is inversely proportional to the heat capacity of the bistable element.

scholarly journals Thermal relaxation of a two-dimensional plasma in a d.c. magnetic field. Part 2. Numerical simulation

1974 ◽  
Vol 12 (1) ◽  
pp. 27-31 ◽  
Author(s):  
Jang-Yu Hsu ◽  
Glenn Joyce ◽  
David Montgomery
Keyword(s):  
Magnetic Field ◽  
Relaxation Time ◽  
Linear Dimension ◽  
Plasma Frequency ◽  
Relaxation Times ◽  
Thermal Relaxation ◽  
Two Dimensional ◽  
Thermal Relaxation Times ◽  
Two Parameters ◽  
Number Of Particles

The thermal relaxation process for a spatially uniform two-dimensional plasma in a uniform d.c. magnetic field is simulated numerically. Thermal relaxation times are defined in terms of the time necessary for the numerically computed Boltzmann H function to decrease through a given part of the distance to its minimum value. Dependence of relaxation time on two parameters is studied: number of particles per Debye square n0 λ2D and ratio of gyrofrequency to plasma frequency Ω/ωp. When Ω2/ω2p becomes ≫[ln (L/2πλD)]−½, where L is the linear dimension of the system, it is found that the relaxation time varies to a good approximation as (n0 λ2D)½ and Ω/ωp.

Correlating Blocking Temperatures in Single Molecule Magnets with Raman Relaxation

2018 ◽  
Author(s):  
Marcus J. Giansiracusa ◽  
Andreas Kostopoulos ◽  
George F. S. Whitehead ◽  
David Collison ◽  
Floriana Tuna ◽  
...  
Keyword(s):  
Relaxation Time ◽  
Single Molecule ◽  
Energy Barrier ◽  
Thermal Relaxation ◽  
Relaxation Mechanism ◽  
Blocking Temperature ◽  
Single Molecule Magnets ◽  
Single Molecule Magnet ◽  
Key Parameter

We report a six coordinate DyIII single-molecule magnet<br>(SMM) with an energy barrier of 1110 K for thermal relaxation of<br>magnetization. The sample shows no retention of magnetization<br>even at 2 K and this led us to find a good correlation between the<br>blocking temperature and the Raman relaxation regime for SMMs.<br>The key parameter is the relaxation time (𝜏<sub>switch</sub>) at the point where<br>the Raman relaxation mechanism becomes more important than<br>Orbach.

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