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Research Papers: Micro/Nanoscale Heat Transfer

Modeling of Thermally Driven Resonance at Multiscales

[+] Author and Article Information
P. Srinivasan1

Department of Mechanical and Aerospace Engineering,  Monash University, Clayton VIC 3800, Australia e-mail: prasanna.srinivasan@monash.eduSchool of Engineering Sciences,  University of Southampton, Southampton SO171BJ, UK

S. Mark Spearing

Department of Mechanical and Aerospace Engineering,  Monash University, Clayton VIC 3800, Australia e-mail: prasanna.srinivasan@monash.eduSchool of Engineering Sciences,  University of Southampton, Southampton SO171BJ, UK

1

Corresponding author.

J. Heat Transfer 133(11), 112402 (Sep 19, 2011) (10 pages) doi:10.1115/1.4004359 History: Received April 11, 2011; Revised May 31, 2011; Published September 19, 2011; Online September 19, 2011

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.

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Copyright © 2011 by American Society of Mechanical Engineers
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Figures

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Figure 1

(a) Schematic of a cantilever beam excited by temperature oscillations within the structure and (b) energy transfer across the control volume considered. q̂x represents the heat flux vector across the cross-section at the location x.

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Figure 2

(a) Modulus and (b) phase of θd(1) for different values of (χ'p)-1 obtained using Eq. 7

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Figure 3

Distribution of real and imaginary components, modulus and phase of dimensionless temperature amplitude for (a) n = 1 and (b) n = 3 at different spatial locations

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Figure 4

(a) Normalized thermal wave trains corresponding to n = 3 for the five different chosen phase values (b) Imaginary components of travelling thermal wave trains corresponding to n = 3 for the five different chosen phase values

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Figure 5

Spatial distribution of the dimensionless temperature amplitude for n = 30

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Figure 6

Effect of Fourier harmonic, n on the probability of achieving thermomechanical resonance

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Figure 7

Micromachined Al-SiX NY bimaterial cantilever structure suspended over a trench. Inset shows the scanning electron micrograph of the cross section of the bimaterial structure

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Figure 8

FE model to predict the resonant frequencies of a beam structure. Two different beam lengths are considered, L = 150 and 160 μm. Inset shows the normalized mode shape corresponding to the fundamental flexural resonant frequency (90.2 kHz and 79.7 kHz for L = 150 and 160 μm, respectively).

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Figure 9

A snap shot of the frequency response of a bimaterial cantilever structure (L = 120 μm) at a particular instant when excited electrothermally by a periodic chirp signal of 0.6V. Plots of (a) amplitude and (b) phase change at the fundamental resonant frequency of 82.82 kHz.

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Figure 10

Time domain response of L = 120 μm structure subjected to a periodic sinusoidal excitation vo  = 0.6V at 41.41 kHz (half of fundamental resonant frequency). (a) N = 12 waves completed one full cycle within the time span of 1.91 ms and (b) time domain response at higher temporal resolution shows oscillation at a time period proportional to the inverse of the resonant frequency.

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Figure 11

Time domain response of (a) L = 40 μm (fundamental mode) (b) L = 160 μm (fundamental mode) and (c) L = 200 μm (second resonant mode: 150.50 kHz) subjected to a periodic sinusoidal excitation of vo  = 0.6 V. The number of waves corresponding to L = 40, 160 and 200 μm are N = 3, 25 and 27, respectively.

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