Viscothermoelastic vibrations in micro-scale beam resonators with linearly varying thickness

2012 ◽  
Vol 90 (5) ◽  
pp. 487-496 ◽  
Author(s):  
D. Grover
Keyword(s):  
Microelectromechanical Systems ◽  
Relaxation Times ◽  
Thermomechanical Coupling ◽  
Damping Factor ◽  
Thermoelastic Damping ◽  
Thin Beam ◽  
Programming Software ◽  
Thermally Conducting ◽  
Matlab Programming ◽  
Analytical Expressions

In this paper the closed form expressions for the transverse vibrations of a homogenous, isotropic, thermally conducting, Kelvin–Voigt type viscothermoelastic thin beam with variable thickness, based on Euler–Bernoulli theory have been derived. The effects of relaxation times, thermomechanical coupling, surface conditions, and beam dimensions on energy dissipation induced by thermoelastic damping in microelectromechanical systems resonators are investigated for beams under clamped and simply supported conditions. Analytical expressions for deflection, temperature change, frequency shifts and thermoelastic damping in the beam have been derived. Some numerical results with the help of MATLAB programming software in the case of silicon nitride have also been presented. The computer simulated results with respect to the damping factor and frequency shift have been presented graphically.

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.

Vibration Analysis of Homogeneous Transradially Isotropic Generalized Thermoelastic Spheres

2011 ◽  
Vol 133 (4) ◽  
Author(s):  
J. N. Sharma ◽  
N. Sharma
Keyword(s):  
Vibration Analysis ◽  
Solid Helium ◽  
Formal Solution ◽  
Thermal Relaxation ◽  
Free Vibration Analysis ◽  
Damping Factor ◽  
Special Cases ◽  
Secular Equations ◽  
Generalized Thermoelastic ◽  
Matlab Programming

The exact free vibration analysis of stress free or rigidly fixed, thermally insulated/isothermal, transradially (spherically) isotropic thermoelastic solid sphere has been presented in context of nonclassical thermoelasticity. The transradially isotropic is also frequently referred as spherically isotropic in the literature. The basic governing equations of linear generalized thermoelastic, transradially isotropic, sphere have been uncoupled and simplified with the help of Helmholtz decomposition theorem. The formal solution of the coupled system of partial differential equations has been obtained by employing matrix Fröbenius method of extended series. The secular equations for the existence of possible modes of vibrations in the sphere have been derived by employing boundary conditions. The special cases of spheroidal (S-mode) and toroidal (T-mode) vibrations have also been deduced and discussed. It is found that the toroidal motion gets decoupled from the spheroidal one and remains independent of thermal variations and thermal relaxation time. In order to illustrate the analytical development, the numerical solution of secular equations for spheroidal motion (S-mode) is carried out with respect of magnesium and solid helium spheres. The lowest frequency and damping factor of vibrational modes have been computed with the help of MATLAB programming and the results are presented graphically. The study may find applications in aerospace, navigation, geophysics tribology, and other industries where spherical structures are in frequent use.

Effect of Rotation to a Half-Sapce in Magneto-Thermoelasticity with Thermal Relaxations

2007 ◽  
Vol 353-358 ◽  
pp. 3018-3021
Author(s):  
Ying Pan ◽  
Zi Hou Zhang ◽  
Li Hou Liu
Keyword(s):  
Magnetic Field ◽  
Half Space ◽  
Normal Mode Analysis ◽  
Relaxation Times ◽  
Generalized Thermoelasticity ◽  
Mode Analysis ◽  
Two Dimensional ◽  
Induced Magnetic Field ◽  
Coupled Problem ◽  
Analytical Expressions

Based on Green and Lindsay’s generalized thermoelasticity theory with two relaxation times, a two-dimensional coupled problem in electromagneto-thermoelasticity for a rotating half-space solid whose surface is subjected to a heat is studied in this paper. The normal mode analysis is used to obtain the analytical expressions for the considered variables. It can be found electromagneto-thermoelastic coupled effect in the medium, and it also can be found that rotation acts to significantly decrease the magnitude of the real part of displacement and stress and insignificantly affect the magnitude of temperature and induced magnetic field.

scholarly journals Modelling Reflection and Transmission of Acoustic Waves at a Semiconductor: Fluid Interface

2012 ◽  
Vol 2012 ◽  
pp. 1-10 ◽  
Author(s):  
A. Sharma ◽  
J. N. Sharma ◽  
Y. D. Sharma
Keyword(s):  
Acoustic Waves ◽  
Grazing Incidence ◽  
Reflection And Transmission Coefficients ◽  
Reflection And Transmission ◽  
Transmission Coefficients ◽  
Saw Devices ◽  
Special Cases ◽  
Gauss Elimination ◽  
Programming Software ◽  
Matlab Programming

The paper concentrates on the study of reflection and transmission characteristics of acoustic waves at the interface of a semiconductor half-space underlying an inviscid liquid. The reflection and transmission coefficients varying with the incident angles are examined. Calculated results are verified by considering the quasilongitudinal () and quasitransverse () waves. The special cases of normal and grazing incidence are also derived and discussed. Finally, the numerical computations of reflection and transmission coefficients are carried out with the help of Gauss elimination method by using MATLAB programming software for silicon (Si) and germanium (Ge) semiconductors. The computer simulated-results have been plotted graphically for Si and presented in tabular form in case of Ge semiconductors. The study may be useful in semiconductors, geology, and seismology in addition to surface acoustic wave (SAW) devices.

scholarly journals Integration of distributed generation and compensating capacitor in radial distribution system via firefly algorithm

2019 ◽  
Vol 16 (1) ◽  
pp. 67 ◽  
Author(s):  
N. Khuan ◽  
S. R. A. Rahim ◽  
M. H. Hussain ◽  
A. Azmi ◽  
S. A. Azmi
Keyword(s):  
Distributed Generation ◽  
Radial Distribution ◽  
Distribution System ◽  
Firefly Algorithm ◽  
Optimal Location ◽  
Voltage Profile ◽  
Radial Distribution System ◽  
Programming Software ◽  
Matlab Programming ◽  
Voltage Profile Improvement

<p>This paper presents an integration of distributed generation and capacitor in radial distribution system via Firefly Algorithm (FA).  In this study, the FA is developed in order to determine the optimal location and size for compensation schemes namely distributed generation (DG) and compensating capacitor (CC). The FA which is a meta-heuristic algorithm is inspired by the flashing behavior of fireflies. The proposed technique was tested on IEEE Reliability Test systems namely the IEEE 69-bus and the program was developed using the MATLAB programming software. The results shown a significant reduction in the line losses and voltage profile improvement has been obtained with the installation of distributed generation and capacitor in the system.</p>

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.

scholarly journals Vibration of circular micro-ceramic (Si3N4) plate resonators in the context of the generalized viscothermoelastic dual-phase-lagging theory

2019 ◽  
Vol 11 (11) ◽  
pp. 168781401988948 ◽  
Author(s):  
Najat A Alghamdi
Keyword(s):  
Aspect Ratio ◽  
Boundary Conditions ◽  
Laplace Transform ◽  
Circular Plate ◽  
Plate Theory ◽  
Relaxation Times ◽  
Mechanical Relaxation ◽  
Dual Phase ◽  
Governing Equations ◽  
Thermally Conducting

In this article, the analysis and numerical results are represented for the thermoelastic of an isotropic homogeneous, thermally conducting, Kelvin–Voigt-type circular micro-plate in the context of Kirchhoff’s Love plate theory of generalized viscothermoelasticity based on the dual-phase-lagging model. The governing equations are obtained for the generalized dual-phase-lagging model and coupled viscothermoelastic plates. The scaled viscothermoelasticity has been illustrated in the case of the circular plate and the axisymmetric circular plate for an aspect ratio for clamped boundary conditions. Laplace transform has been applied, and its inversions have been calculated numerically by using the Tzou method. The results have been carried out for the ceramic (Si3N4). It is noted that the temperature increment and lateral deflection are significantly affected by the time, the width, the thickness, and the mechanical relaxation times of the material.

scholarly journals Effects of Rotation and Gravity Field on Surface Waves in Fibre-Reinforced Thermoelastic Media under Four Theories

2013 ◽  
Vol 2013 ◽  
pp. 1-20 ◽  
Author(s):  
A. M. Abd-Alla ◽  
S. M. Abo-Dahab ◽  
A. Al-Mullise
Keyword(s):  
Surface Waves ◽  
Rayleigh Waves ◽  
Relaxation Times ◽  
Type Ii ◽  
Physical Domain ◽  
Stoneley Waves ◽  
Harmonic Vibrations ◽  
Effects Of Rotation ◽  
Analytical Expressions ◽  
Thermoelastic Theory

Estimation is done to investigate the gravitational and rotational parameters effects on surface waves in fibre-reinforced thermoelastic media. The theory of generalized surface waves has been firstly developed and then it has been employed to investigate particular cases of waves, namely, Stoneley waves, Rayleigh waves, and Love waves. The analytical expressions for surface waves velocity and attenuation coefficient are obtained in the physical domain by using the harmonic vibrations and four thermoelastic theories. The wave velocity equations have been obtained in different cases. The numerical results are given for equation of coupled thermoelastic theory (C-T), Lord-Shulman theory (L-S), Green-Lindsay theory (G-L), and the linearized (G-N) theory of type II. Comparison was made with the results obtained in the presence and absence of gravity, rotation, and parameters for fibre-reinforced of the material media. The results obtained are displayed by graphs to clear the phenomena physical meaning. The results indicate that the effect of gravity, rotation, relaxation times, and parameters of fibre-reinforced of the material medium is very pronounced.

Exact Solution of Thermoelastic Damping and Frequency Shifts in a Nano-Beam Resonator

2015 ◽  
Vol 15 (06) ◽  
pp. 1450082 ◽  
Author(s):  
Ibrahim A. Abbas
Keyword(s):  
Exact Solution ◽  
Natural Frequencies ◽  
Thermoelastic Damping ◽  
Frequency Shifts ◽  
Beam Resonator ◽  
Simply Supported ◽  
Thermoelastic Vibration ◽  
Modes Of Vibration ◽  
Generalized Thermoelastic ◽  
Analytical Expressions

In this study, we consider the problem of a generalized thermoelastic vibration of a bounded nano-beam resonator in the context of Green and Naghdi theory (GNIII). The first four modes of vibration in the nano-beam resonator are investigated for the beam under clamped and simply supported conditions. Analytical expressions for the deflection, temperature change, frequency shifts, and thermoelastic damping in the beam are derived. The numerical results have been presented graphically in respect of natural frequencies, thermoelastic damping and frequency shift.

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