Thermoelastic Actuation: Solution for Circular Composite Plates With Application in MEMS

2002 ◽  
Author(s):  
Venkataraman Chandrasekaran ◽  
Mark Sheplak ◽  
Louis N. Cattafesta ◽  
Bhavani V. Sankar
Keyword(s):  
Heat Conduction ◽  
Joule Heating ◽  
Plate Theory ◽  
Composite Plates ◽  
Mechanical Analysis ◽  
Conduction Model ◽  
Time Harmonic ◽  
Out Of Plane ◽  
Fourier Heat Conduction ◽  
Analytical Expressions

This paper presents the dynamic analysis of a thermoelastically actuated circular composite diaphragm, for MEMS applications. The diaphragm is used as an acoustic transmitter, actuated at ultrasonic frequencies via a diffused surface heater at its center. The principle of operation of the thermal actuator is the generation of an oscillating temperature gradient across the diaphragm cross-section due to Joule heating of the diffused heater, creating a thermal moment that results in out-of-plane bending of the diaphragm. The mechanical analysis of the diaphragm, modeled as a composite plate, is based on the classical laminated plate theory. The time harmonic heat conduction resulting from the Joule heating of the diffused surface heater, modeled as a surface heat flux input, is analyzed using the Fourier heat conduction model. Analytical expressions have been obtained for the temperature distribution, and the resulting thermal moment, and plate deflection.

scholarly journals Nonlinear Solution to a Non-Fourier Heat Conduction Problem in a Slab Heated by Laser Source

2016 ◽  
Vol 63 (1) ◽  
pp. 129-144
Author(s):  
Mohammad Javad Noroozi ◽  
Seyfolah Saedodin ◽  
Davood Domiri Ganji
Keyword(s):  
Heat Conduction ◽  
Heat Conduction Problem ◽  
Adomian Decomposition Method ◽  
Laser Source ◽  
Temperature Dependent ◽  
Conduction Model ◽  
Non Linear Equation ◽  
Adomian Decomposition ◽  
Non Linear ◽  
Fourier Heat Conduction

Abstract The effect of laser, as a heat source, on a one-dimensional finite body was studied in this paper. The Cattaneo-Vernotte non-Fourier heat conduction model was used for thermal analysis. The thermal conductivity was assumed temperature-dependent which resulted in a non-linear equation. The obtained equations were solved using the approximate-analytical Adomian Decomposition Method (ADM). It was concluded that the non-linear analysis is important in non-Fourier heat conduction problems. Significant differences were observed between the Fourier and non-Fourier solutions which stresses the importance of non-Fourier solutions in the similar problems.

scholarly journals Non-Fourier Heat Conduction of a Functionally Graded Cylinder Containing a Cylindrical Crack

2020 ◽  
Vol 2020 ◽  
pp. 1-11 ◽  
Author(s):  
Jiawei Fu ◽  
Keqiang Hu ◽  
Linfang Qian ◽  
Zengtao Chen
Keyword(s):  
Heat Flux ◽  
Heat Conduction ◽  
Intensity Factor ◽  
Functionally Graded ◽  
Conduction Model ◽  
Heat Conduction Model ◽  
Flux Intensity ◽  
Cylindrical Crack ◽  
Heat Flux Intensity ◽  
Fourier Heat Conduction

The present work investigates the problem of a cylindrical crack in a functionally graded cylinder under thermal impact by using the non-Fourier heat conduction model. The theoretical derivation is performed by methods of Fourier integral transform, Laplace transform, and Cauchy singular integral equation. The concept of heat flux intensity factor is introduced to investigate the heat concentration degree around the crack tip quantitatively. The temperature field and the heat flux intensity factor in the time domain are obtained by transforming the corresponding quantities from the Laplace domain numerically. The effects of heat conduction model, functionally graded parameter, and thermal resistance of crack on the temperature distribution and heat flux intensity factor are studied. This work is beneficial for the thermal design of functionally graded cylinder containing a cylindrical crack.

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.

Nonlinear analysis of a non-Fourier heat conduction problem in a living tissue heated by laser source

2017 ◽  
Vol 10 (08) ◽  
pp. 1750107 ◽  
Author(s):  
Mohammad Javad Noroozi ◽  
Majid Goodarzi
Keyword(s):  
Heat Conduction ◽  
Nonlinear Analysis ◽  
Heat Conduction Problem ◽  
Adomian Decomposition Method ◽  
Experimental Result ◽  
Laser Source ◽  
Living Tissue ◽  
Conduction Model ◽  
Adomian Decomposition ◽  
Fourier Heat Conduction

The effect of laser, as a heat source, on a one-dimensional finite living tissue was studied in this paper. The dual phase lagging (DPL) non-Fourier heat conduction model was used for thermal analysis. The thermal conductivity was assumed temperature-dependent, resulting in a nonlinear equation. The obtained equations were solved using the approximate-analytical Adomian decomposition method (ADM). It was concluded that the nonlinear analysis was important in non-Fourier heat conduction problems. Moreover, a good agreement between the present nonlinear model and experimental result was obtained.

Warpage of Flip Chip BGA Package

2006 ◽  
Author(s):  
Milena Vujosevic
Keyword(s):  
Flip Chip ◽  
Plate Theory ◽  
Contour Plot ◽  
Thermally Induced ◽  
Ball Grid Arrays ◽  
Fundamental Understanding ◽  
Out Of Plane ◽  
Bga Package ◽  
Plane Displacement ◽  
Analytical Expressions

The work focuses on the thermally induced out of plane displacement of Flip Chip Ball Grid Arrays (FCBGA). Analytical expressions for substrate displacements are derived based on the Plate Theory and Suhir's solution for stresses in tri-material assembly. The validity of the model is established by comparing the analytical solution to the finite element results as well as to the experimental data. The benefits of the model are twofold: 1) it provides a tool for fundamental understanding of the parameters that influence warpage, and 2) has a predictive capability. With respect to 1) an analysis is presented on the nature and degree of influence that different geometric and material parameters have on the FCBGA warpage. With respect to 2) the "Warpage Contour Plot" is proposed as a tool for warpage prediction that can be easily utilized in the early stages of the design process.

Analysis of a Composite Piezoelectric Circular Plate With Initial Stresses for MEMS

2002 ◽  
Author(s):  
Guiqin Wang ◽  
Bhavani V. Sankar ◽  
Louis N. Cattafesta ◽  
Mark Sheplak
Keyword(s):  
Composite Plate ◽  
Plate Theory ◽  
Composite Plates ◽  
Mechanical Analysis ◽  
Initial Stresses ◽  
Piezoelectric Composite ◽  
Mems Devices ◽  
Design And Optimization ◽  
Transverse Pressure ◽  
Analytical Result

The paper presents a mechanical analysis of the multi-layer circular composite plate For MEMS devices. Each layer of the plate is assumed to have different radius, material properties and initial stresses. Governing equations for the composite plate are derived based on the classical laminated plate theory, and analytical soultions have been developed for static deflection of the initially stressed plate due to transverse pressure loading as well as for a given electric field in the piezoelectric layer. A nonlinear finite elernent analysis of the plate is also performed. The analytical result match the FE results for the range of parameters used in the microphone design. The analytical model will be useful in the design and optimization of MEMS devices containing circular piezoelectric composite plates and diaphragms.

Theoretical 3D Model of Thermoelastic Damping in Laminated Rectangular Plate Resonators

2018 ◽  
Vol 18 (12) ◽  
pp. 1850158 ◽  
Author(s):  
Shoubin Liu ◽  
Jingxuan Ma ◽  
Xianfeng Yang ◽  
Yuxin Sun ◽  
Jialing Yang ◽  
...  
Keyword(s):  
Heat Conduction ◽  
Energy Loss ◽  
Rectangular Plate ◽  
Governing Equation ◽  
Elastic Strain Energy ◽  
Laminated Plates ◽  
Thermoelastic Damping ◽  
Conduction Model ◽  
Out Of Plane ◽  
Energy Dissipated

Thermoelastic damping (TED) can lead to energy loss in microscale resonators, which is an intrinsic mechanism. To minimize the energy loss, it is required to determine the TED of resonators. Laminated plate resonators are commonly used in practice. However, existing researches on TED of the laminated resonators use mainly the one-dimensional (1D) heat conduction model, as the 3D governing equation is complicated, which cannot show the influences of boundary conditions along the supporting edges. In this paper, the governing equation of thermoelastic problems with 3D heat conduction was established for the out-of-plane vibration of the laminated rectangular plate. The analytical expression of the TED was derived using its physical meaning, namely, the ratio of the energy dissipated to the total elastic strain energy stored per cycle of vibration. It was found that the size and shape of the plate affect crucially the TED. The values of TED for higher-order vibration modes were also evaluated. Most importantly, the influences of supporting conditions and heat conduction conditions along the four edges were studied, which is the first report for laminated plates. The present approach can provide guidance for the design of high-quality bilayered resonators.

scholarly journals Estimating Relaxation Time and Fractionality Order Parameters in Fractional Non-Fourier Heat Conduction Using Conjugate Gradient Inverse Approach in Single and Three-Layer Skin Tissues

Processes ◽  
2021 ◽  
Vol 9 (11) ◽  
pp. 1877
Author(s):  
Piran Goudarzi ◽  
Awatef Abidi ◽  
Seyed Abdollah Mansouri Mehryan ◽  
Mohammad Ghalambaz ◽  
Mikhail A. Sheremet
Keyword(s):  
Heat Conduction ◽  
Conjugate Gradient ◽  
Inverse Method ◽  
Single Layer ◽  
Constant Heat Flux ◽  
Phase Lag ◽  
Unknown Parameters ◽  
Conduction Model ◽  
Inverse Approach ◽  
Fourier Heat Conduction

In this work, the relaxation parameter (τ) and fractionality order (α) in the fractional single phase lag (FSPL) non-Fourier heat conduction model are estimated by employing the conjugate gradient inverse method (CGIM). Two different physics of skin tissue are chosen as the studied cases; single and three-layer skin tissues. Single-layer skin is exposed to laser radiation having the constant heat flux of Qin. However, a heat pulse with constant temperature is imposed on the three-layer skin. The required inputs for the inverse problem in the fractional diffusion equation are chosen from the outcomes of the dual phase lag (DPL) theory. The governing equations are solved numerically by utilizing implicit approaches. The results of this study showed the efficiency of the CGIM to estimate the unknown parameters in the FSPL model. In fact, obtained numerical results of the CGIM are in excellent compatibility with the FSPL model.

Absence of Oscillations and Resonance in Porous Media Dual-Phase-Lagging Fourier Heat Conduction

2005 ◽  
Vol 127 (3) ◽  
pp. 307-314 ◽  
Author(s):  
Peter Vadasz
Keyword(s):  
Porous Media ◽  
Heat Conduction ◽  
Thermal Equilibrium ◽  
Local Thermal Equilibrium ◽  
Dual Phase ◽  
Thermal Waves ◽  
Conduction Model ◽  
Physical Conditions ◽  
Fourier Heat Conduction ◽  
Thermal Oscillations

The approximate equivalence between the dual-phase-lagging heat conduction model and the Fourier heat conduction in porous media subject to lack of local thermal equilibrium suggested the possibility of thermal oscillations and resonance. The present investigation demonstrates that the physical conditions necessary for such thermal waves and, possibly resonance, to materialize are not attainable in a porous slab subject to constant temperature conditions applied on the boundaries.

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