Abstract
Understanding the mechanisms of thermally driven resonance is a key for designing many engineering and physical systems especially at small scales. This paper focuses on the modeling aspects of such phenomena using the classical Fourier diffusion theory. Critical analysis revealed that the thermally induced resonant excitation is characterized by the generation of multiple wave trains with a constant phase shift as opposed to the single standing wave generated in a mechanically driven resonant response. The hypothesis proposed herein, underpin a broad range of scientific and technological developments and the analytical treatment enables design of thermally driven resonant systems with improved performance.
Issue Section:
Micro/Nanoscale Heat
Transfer
Keywords:
thermal wave,
resonance,
phonons,
multiscales,
diffusion,
flow simulation,
Fourier analysis,
heat transfer,
resonance,
vibrations
References
1.
Burg
, T. P.
, Godin
, M.
, Knudsen
, S. M.
, Shen
, W.
, Carlson
, G.
, Foster
, J. S.
, Babcock
, K.
, and Manalis
, S. R.
, 2007, “Weighing of Biomolecules, Single Cells and Single Nano Particles in Fluid
,” Nature (London)
, 446
, pp. 1066
–1069
. 2.
Burg
, T. P.
, Sader
, J. E.
, and Manalis
, S. R.
, 2009, “Nonmonotonic Energy Dissipation in Microfluidic Resonators
,” Phys. Rev. Lett.
, 102
, p. 228103
. 3.
Seshia
, A. A.
, Howe
, R. T.
, and Montague
, S.
, 2002 “An Integrated Microelectromechanical Resonant Output Gyroscope
,” 15th IEEE Micro-Electro-Mechanical Systems Conference
, pp. 722
–726
.4.
Roessig
, T. A.
, Howe
, R. T.
, Pisano
, A. P.
, and Smith
, J. H.
, 1997, “Surface Micromachined Resonant Accelerometer
,” Int. Conf. Solid-State Sens. Actuators
, 2
, pp. 859
–862
. 5.
Seshia
, A. A.
, Palaniapan
, M.
, Roessig
, T. A.
, Howe
, R. T.
, Gooch
, R. W.
, Schimert
, T. R.
, and Montague
, S.
, 2002, “A Vacuum Packaged Surface Micromachined Resonant Accelerometer
,” J. Microelectromech. Syst.
, 11
(6
), pp. 784
–793
. 6.
Piazza
, G.
, Stephanou
, P. J.
, and Pisano
, A. P.
, 2006, “Piezoelectric Aluminum Nitride Vibrating Contour-Mode Mems Resonators
,” J. Microelectromech. Syst.
, 16
(6
), pp. 1406
–1418
. 7.
Manzaneque
, T.
, Hernando
, J.
, Rodriguez-Aragon
, L.
, Ababneh
, A.
, Seidel
, H.
, Schmid
, U.
, and Sanchez-Rojas
, J. L.
, 2010, “Analysis of the Quanlity Factor of AIN-Actuated Micro-Resonators in Air and Liquid
,” Microsyst. Technol.
, 16
(5
), pp. 837
–645
. 8.
Tanski
, W.
, 1979, “Surface Acoustic Wave Resonators on Quartz
,” IEEE Trans. Sonics Ultrason.
, SU-26
(2
), pp. 93
–104
.9.
Tilmans
, H. A. C.
, Elwenspoek
, M.
, and Fluitman
, J. H. J.
, 1992, “Microresonant Force Gauges
,” Sens. Actuators, A
, 30
(1–2
), pp. 35
–53
. 10.
Lammerink
, T. S. J.
, Elwenspoek
, M.
, Van Ouwerkerk
, R. H.
, Bouwstra
, S.
, and Fluitman
, J. H.
, 1990, “Performance of Thermally Excited Resonators
,” Sens. Actuators A
, 21
(1–3
), pp. 352
–356
. 11.
Brand
, O.
, and Baltes
, H.
, 1993, “Thermally Excited Silicon Oxide Beam and Bridge Resonators in CMOS technology
,” IEEE Trans. Electron Devices
, 40
(10
), pp. 1745
–1753
. 12.
Jiang
, L.
, Cheung
, R.
, Hedley
, J.
, Hassan
, M.
, Harris
, A. J.
, Burdess
, J. S.
, Mehregany
, M.
, and Zorman
, C. A.
, 2006, “SiC Cantilever Resonators With Electrothermal Actuation
,” 128
(2
), pp. 376
–386
.13.
Rahafrooz
, A.
, Hajjam
, A.
, Tousifar
, B.
, and Pourkamali
, S.
, 2010, “Thermal Actuation, a Suitable Mechanism for High Frequency Electromechanical Resonators
,” IEEE 23rd International Conference on Microelectromechanical Systems
, pp. 200
–203
.14.
Tzou
, D. Y.
, 1992, “Damping and Resonance Characteristics of ThermalWaves
,” Trans. ASME
, 59
, pp. 862
–867
15.
Kulish
, V. V.
, and Novozhilov
, V. B.
, 2003, “The Relationship Between the Local Temperature and the Local Heat Flux Within a One-Dimensional Semi-Infinite Domain Of Heat Wave Propagation
,” Math. Probl. Eng.
, 2003
(4
), pp. 173
–179
. 16.
Huber
, J. E.
, Fleck
, N. A.
, and Ashby
, M. F.
, 1997, “The Selection of Mechanical Actuators Based on Performance
,” Proc. R. Soc. London A
, 453
, pp. 2185
–2205
. 17.
Volz
, S.
, Saulnier
, J. B.
, and Lallemand
, M.
, 1996, “Transient Fourier-Law Deviation by Molecular Dynamics in Solid Argon
,” Phys. Rev. B
, 54
(1
), pp. 340
–347
. 18.
Kaminski
, W.
, 1990, “Hyperbolic Heat Conduction Equation for Materials With a Nonhomogeneous Inner Structure
,” ASME J. Heat Transfer
, 112
, pp. 555
–560
. 19.
Schatz
, G. C.
, 1978, “A Generalised Langevin Approach to Molecular Collision Dynamics
,” Chem. Phys.
, 31
(2
), pp. 295
–307
. 20.
Toombs
, G. A.
, Sheard
, F. W.
, Neilson
, D.
, and Challis
, L. J.
, 1987, “Phonon Emission by a Hot Two-Dimensional Electron Gas in a Quantizing Magnetic Field
,” Solid State Commun.
, 64
(4
), pp. 577
–581
. 21.
Srinivasan
, P.
, and Spearing
, S. M.
, 2007, “Materials Selection and Design of Microlectrothermal Bimaterial Actuators
,” J. Microelectromech. Syst.
, 16
(2
), pp. 248
–259
. 22.
Srinivasan
, P.
, 2008, “Materials Selection for Microsystems Actuators
,” Ph.D.x thesis, pp. 164
–170
.23.
Voltera
, E.
, and Zachmanoglou
, E. C.
, 1965, Dynamics of Vibrations
, Charles E. Merrill Books, Inc.
, Columbus, OH
.24.
Mader
, M. P.
, 2000, Condensed Matter Physics
, John Wiley and Sons
, New York
.25.
Tzou
, D. Y.
, 1996, Macro- to Micro-scale Heat Transfer
, Taylor & Francis
, Washington, DC
.26.
Xu
, J.
, and Wang
, X.
, 2002, “Simulation of Ballistic and Non-Fourier Thermal Transport in Ultra-Fast Laser Heating
,” Physica B
, 351
, pp. 213
–226
. 27.
Barletta
, A.
, and Zanchini
, E.
, 1997, “Hyperbolic Heat Conduction and Local Equilibrium: A Second Law Analysis
,” Int. J. Heat Mass Transfer
, 40
(5
), pp. 1007
–1016
. 28.
Chen
, G.
, 2000, “Particularities of Heat Conduction in Nanostructures
,” J. Nanoparticle Res.
, 2
, pp. 199
–204
. 29.
Gendelman
, O. V.
, and Savin
, A. V.
, 2010, “Nonstationary Heat Conduction in One-Dimensional Chains With Conserved Momentum
,” Phys. Rev. E
, 81
, p. 020103
. 30.
Aksamija
, Z.
, and Ravaioli
, U.
, 2006, “Joule Heating and Phonon Transport in Silicon MOSFETs
,” J. Comput. Electron.
, 5
(4
), pp. 431
–434
. 31.
Lin
, Z.
, and Zhigilei
, 2008, “Electron-Phonon Coupling and Electron Heat Capacity of Metals Under Conditions of Strong Electron-Phonon Nonequilibrium
,” Phys. Rev. B
, 77
, p. 075133
. 32.
Tzou
, D. Y.
, 1992, “Thermal Resonance Under Frequency Excitation
,” Trans. ASME
, 114
, pp. 310
–316
. 33.
Biedermann
, L. B.
, Tung
, R. C.
, Raman
, A.
, and Reifenberger
, R. G.
, 2009, “Flexural Vibration Spectra of Carbon Nanotubes Measured Using Laser Doppler Vibrometry
,” 20
, p. 035702
.34.
Huth
, H.
, Schnell
, M.
, Wittborn
, J.
, Ocelic
, N.
, and Hillenbrand
, R.
, 2011, “Infrared-Spectroscopic Nanoimaging With a Thermal Source
,” Nature Mater.
, 10
, pp. 352
–356
. 35.
Chou
, J.
, Han
, Y.
, and Jalali
, B.
, 2003, “Adaptive RF-Photonic Arbitrary Waveform Generator
,” IEEE Photonics Technol. Lett.
, 15
(4
), pp. 581
–583
. 36.
Nguyen
, C. T.C
, 1995, “Micromechanical Resonators for Oscillators and Filters
,” Proceedings of IEEE Ultrasonics Symposium
, Vol. 1
, pp. 489
–499
.37.
Ashby
, M. F.
, 1993, Materials Selection in Mechanical Design
, 1st ed., Pergamon
, Oxford, UK
.Copyright © 2011
by American Society of Mechanical Engineers
You do not currently have access to this content.