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.

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 The reflection phenomena ofSV-waves in a generalized thermoelastic medium

2000 ◽  
Vol 23 (8) ◽  
pp. 529-546 ◽  
Author(s):  
Abo-El-Nour N. Abd-Alla ◽  
Amira A. S. Al-Dawy
Keyword(s):  
Thermal Effect ◽  
Elastic Waves ◽  
Plane Waves ◽  
Relaxation Times ◽  
Thermal Relaxation ◽  
Reflection Coefficients ◽  
Angle Of Incidence ◽  
Special Cases ◽  
Thermal Relaxation Times ◽  
Generalized Thermoelastic

We discuss the reflection of thermoelastic plane waves at a solid half-space nearby a vacuum. We use the generalized thermoelastic waves to study the effects of one or two thermal relaxation times on the reflection plane harmonic waves. The study considered the thermal and the elastic waves of small amplitudes in a homogeneous, isotropic, and thermally conducting elastic solid. The expressions for the reflection coefficients, which are the ratio of the amplitudes of the reflected waves to the amplitude of the incident waves are obtained. It has been shown, analytically, that the elastic waves are modified due to the thermal effect. The reflection coefficients of a shear wave that incident from within the solid on its boundary, which depend on the thermoelastic coupling factor and included the thermal relaxation times, have been found in the general case. The numerical values of reflection coefficients against the angle of incidence for different values of thermal relaxation times have been calculated and the results are given in the form of graphs. Some special cases of reflection have also been discussed, for example, in the absence of thermal effect our results reduce to the ordinary pure elastic case.

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.

Stoneley Wave Generation in Joined Materials With and Without Thermal Relaxation Due to Thermal Mismatch

2007 ◽  
Vol 74 (5) ◽  
pp. 1019-1025 ◽  
Author(s):  
L. M. Brock
Keyword(s):  
Relaxation Time ◽  
Heat Conduction ◽  
Thermal Relaxation ◽  
Interface Temperature ◽  
Stoneley Wave ◽  
Asymptotic Results ◽  
Time Step ◽  
Conduction Model ◽  
Special Cases ◽  
Fourier Heat Conduction

Two perfectly bonded, thermoelastic half-spaces differ only in their thermal parameters. Their governing equations include as special cases the Fourier heat conduction model and models with either one or two thermal relaxation times. An exact solution in transform space for the problem of line loads applied to the interface is obtained. Even though the elastic properties of the half-spaces are identical, a Stoneley function arises, and conditions for the existence of roots are more restrictive than for the isothermal case of two elastically dissimilar half-spaces. Moreover, roots may be either real or imaginary. An exact expression for the time transform of the Stoneley residue contribution to interface temperature change is derived. Asymptotic results for the inverse that, valid for either very short or very long times after load application, is obtained and show that, for long times, residue contributions for all three special cases obey Fourier heat conduction. Short-time results are sensitive to case differences. In particular, a time step load produces a propagating step in temperature for the Fourier and double-relaxation time models, but a propagating impulse for the single-relaxation time model.

Analysis of Deep Levels in GaAs Detector Diodes Using Impedance Spectroscopy

1993 ◽  
Vol 302 ◽  
Author(s):  
C Eiche ◽  
M Fiederle ◽  
J Weese ◽  
D Maier ◽  
D Ebling ◽  
...  
Keyword(s):  
Cross Section ◽  
Regularization Method ◽  
Capture Cross Section ◽  
Relaxation Times ◽  
Thermal Relaxation ◽  
Simulated Data ◽  
Deep Levels ◽  
Admittance Spectroscopy ◽  
Thermal Relaxation Times ◽  
Level 2

ABSTRACTImpedance or admittance spectroscopy has been shown to be a very convenient tool for the investigation of deep levels in semiconductor junctions. At constant temperature a frequency sweep is performed. After that the impedance signal is analysed by a regularization method based on Tikhonov regularization in order to obtain the thermal relaxation times of the deep levels present in the junction. The high resolution of the regularization method in comparison to conventional techniques is demonstrated using simulated data. The temperature dependence of the thermal relaxation times provides information about the properties of the deep levels such as activation energy or capture cross section. Two donor levels with activation energies dE1 =0.58 eV and dE2 =0.68 eV are observed in our detector diodes. It can be shown that the concentration of level 2 is increased after irradiation.

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