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 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.

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.

Thermoelastic Damping of the Axisymmetric Vibration of Laminated Trilayered Circular Plate Resonators

2013 ◽  
Vol 313-314 ◽  
pp. 600-603 ◽  
Author(s):  
Yu Xin Sun ◽  
Yan Jiang ◽  
Jia Ling Yang
Keyword(s):  
Boundary Conditions ◽  
Circular Plate ◽  
Plate Theory ◽  
Axisymmetric Vibration ◽  
Laminated Plate ◽  
Thermoelastic Damping ◽  
Governing Equations ◽  
Out Of Plane ◽  
Laminated Circular Plate ◽  
Thermoelastic Problems

In this paper, thermoelastic damping of the axisymmetric vibration of laminated circular plate resonators will be discussed. Based on the classical laminated plate theory assumptions, the governing equations of coupled thermoelastic problems are established for axisymmetric out-of-plane vibration of trilayered circular plate with fully clamped boundary conditions. The analytical expression for thermoelastic damping is obtained and the accuracy is verified through comparison with FEM results.

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.

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.

Thermoelastic damping of the axisymmetric vibration of laminated trilayered circular plate resonators

2014 ◽  
Vol 92 (9) ◽  
pp. 1026-1032 ◽  
Author(s):  
Yuxin Sun ◽  
Yan Jiang ◽  
Jialing Yang
Keyword(s):  
Circular Plate ◽  
Volume Fraction ◽  
Material Selection ◽  
Plate Theory ◽  
Axisymmetric Vibration ◽  
Thermoelastic Damping ◽  
Loss Mechanism ◽  
Out Of Plane ◽  
Laminated Circular Plate ◽  
Thermoelastic Problems

Thermoelastic damping is a critical loss mechanism in micromachined resonators used for sensing and communication applications. In this paper, thermoelastic damping of the axisymmetric vibration of laminated circular plate resonators will be discussed. Based on the classical laminated plate theory assumptions, the governing equations of coupled thermoelastic problems are established for axisymmetric out-of-plane vibration of trilayered circular plate with fully clamped boundary conditions. The analytical expression for thermoelastic damping is obtained and the accuracy is verified through comparison with FEM results. Then the effect of material selection and the volume fraction of the covering layers are numerically evaluated. Finally, the thermoelastic damping for different vibration modes is also evaluated.

scholarly journals Shock Structure and Relaxation in the Multi-Component Mixture of Euler Fluids

Symmetry ◽  
2021 ◽  
Vol 13 (6) ◽  
pp. 955
Author(s):  
Damir Madjarević ◽  
Milana Pavić-Čolić ◽  
Srboljub Simić
Keyword(s):  
Relaxation Times ◽  
Thermal Relaxation ◽  
Collision Operator ◽  
Weak Form ◽  
Shock Structure ◽  
Theory Approach ◽  
Component Mixture ◽  
Single Temperature ◽  
The Difference ◽  
Euler Fluids

The shock structure problem is studied for a multi-component mixture of Euler fluids described by the hyperbolic system of balance laws. The model is developed in the framework of extended thermodynamics. Thanks to the equivalence with the kinetic theory approach, phenomenological coefficients are computed from the linearized weak form of the collision operator. Shock structure is analyzed for a three-component mixture of polyatomic gases, and for various combinations of parameters of the model (Mach number, equilibrium concentrations and molecular mass ratios). The analysis revealed that three-component mixtures possess distinguishing features different from the binary ones, and that certain behavior may be attributed to polyatomic structure of the constituents. The multi-temperature model is compared with a single-temperature one, and the difference between the mean temperatures of the mixture are computed. Mechanical and thermal relaxation times are computed along the shock profiles, and revealed that the thermal ones are smaller in the case discussed in this study.

scholarly journals Applications of Cattaneo–Christov fluxes on modelling the boundary value problem of Prandtl fluid comprising variable properties

2021 ◽  
Vol 11 (1) ◽  
Author(s):  
Umar Nazir ◽  
Muhammad Sohail ◽  
Umair Ali ◽  
El-Sayed M. Sherif ◽  
Choonkil Park ◽  
...  
Keyword(s):  
Magnetic Parameter ◽  
Fluid Model ◽  
Relaxation Times ◽  
Thermal Relaxation ◽  
Coupled System ◽  
Temperature Fields ◽  
Fluid Temperature ◽  
Variable Properties ◽  
Cartesian Coordinate ◽  
And Diffusion

AbstractStretched flows have numerous applications in different industrial, biomedical and engineering processes. Current research is conducted to examine the flow phenomenon of Prandtl fluid model over a moveable surface. The phenomenon of mass and thermal transportation is based on generalized theory of Cattaneo–Christov which considers the involvement of relaxation times. In addition to these, variable characteristics of thermal conductivity and diffusion coefficient are considered as a function of temperature. The physical problem in Cartesian coordinate system is modeled via boundary layer theory which yields a coupled system of partial differential equations. Group scaling transportation is applied to model these PDEs system. The converted equations have been approximated via optimal homotopic scheme. The efficiency and validity of used approach has been shown by computing the error analysis and establishing a comparative study. It is noted that the enhancement in magnetic parameter plays a controlling role for velocity field and it augment the concentration and temperature fields. Furthermore, increase in thermal relaxation parameter and Prandtl number maintains the fluid temperature.

A In Situ Measuring Method for Stress Gradient of a MEMS Film

2009 ◽  
Vol 60-61 ◽  
pp. 357-360 ◽  
Author(s):  
Han Chen ◽  
Hua Rong ◽  
Ming Wang
Keyword(s):  
Thin Film ◽  
Circular Plate ◽  
Stress Gradient ◽  
Measuring Method ◽  
Mechanical Parameter ◽  
Curvature Radius ◽  
Mems Devices ◽  
Out Of Plane

The stress gradient of a deposited thin-film is a mechanical parameter that affects the performance of MEMS devices, so in-situ measuring stress gradient of a thin-film is great significant. A new in-situ measuring method based on a center-anchored circular plate is presented. The Mirau interferometer has been used to measure the out-of-plane height at the edge of circular plate, then the curvature radius of the plate and the stress gradient of the film can be calculated. The measuring method has been verified by CoventorWare. The accuracy of the presented measuring method is ideal. The advantages of the method also have been discussed.

Sign in / Sign up

Export Citation Format

Share Document