Analysis of Detection Enhancement Using Microcantilevers with Long-Slit-Based Sensors
Abstract
:1. Introduction
2. Theoretical Analysis
2.1. The Typical Rectangular Microcantilever
2.1.1. Deflections of the Typical Rectangular Microcantilever
2.1.1.1. Concentrated Force Loading
2.1.1.2. Prescribed Differential Surface Stress
2.1.2. The Disturbance in the Deflections of the Typical Rectangular Microcantilever
2.2. The Rectangular Microcatilever with a Long-slit
2.2.1. Deflections of the Rectangular Microcatilever with Long-slit
2.2.1.1. Concentrated Force Loadings
2.2.1.2. Prescribed Differential Surface Stress
2.2.2. The Disturbance in the Deflections of the Rectangular Microcantilever with Long-slit
3. Results and Discussion
3.1. Validation of the Results
3.2. Discussion of the Results
3.2.1. Discussion of the Results of First Detection Enhancement Indicator
3.2.2. Discussion of the Results of Clearness Indicator of Typical Rectangular Microcantilever
3.2.3. Discussion of the Results of Second Detection Enhancement Indicator
4. Conclusions
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Nomenclature | |
---|---|
c | clearance length for rectangular microcantilever with long-slit (μm) |
d | microcantilever thickness (μm) |
E | elastic modulus (N μm−2) |
F | concentrated force (N) |
I | area moment of inertia (μm4) |
k | stiffness (N/μm) |
L | typical rectangular microcantilever or slit length (μm) |
Lo | length of rectangular microcatilever with long-slit (μm) |
M | moment (N μm) |
m | mass (kg) |
n | surface stress model index |
Po | dynamic disturbance force per square of frequency of disturbance (N s−2) |
t | time variable (s) |
W | total microcantilever width (μm) |
x | axis of the extension dimension (μm) |
Y | effective elastic modulus (N μm−2) |
Z | first deflection indicator |
z | deflection (μm) |
zd | Amplitude of disturbance in deflection (μm) |
Greek Symbols | |
---|---|
χ | detection clearness indicator |
δ | slit thickness (μm) |
γ1 | the first detection enhancement indicator |
γ2 | the second detection enhancement indicator |
λ | wavelength of the dynamic disturbance (μm) |
ν | Poisson's ratio |
σ | surface stress (N μm−1) |
ω | dynamic disturbance frequency (s−1) |
ωo | first natural frequency of typical rectangular microcantilever (s−1) |
ωs | first natural frequency of rectangular microcantilever with long-slit (s−1) |
Subscripts | |
---|---|
d | disturbance |
F | concentrated force condition |
Δσ | prescribed surface stress condition |
eff | effective value |
Abbreviations | |
---|---|
LB | left beam of the rectangular microcantilever with long-slit |
RB | right beam of the rectangular microcantilever with long-slit |
(d/L) | 10−2 | 10−3 | 10−4 | 10−5 |
---|---|---|---|---|
[(zF)max∣LB/d]γF=1 | 23.928 | 246.81 | 2,490.1 | 24,969 |
[(zF)max∣LB/d]γF=1 = 0.23467 ×exp(−1.00593×d/L) |
n | (d/L) | [(zΔσ)max∣LB/d]∣γΔσ=1 | n | (d/L) | [(zΔσ)max|LB/d]∣γΔσ=1 |
---|---|---|---|---|---|
n = 0 | 10−2 | 21.157 | n = 1.0 | 10−2 | 7.4114 |
10−3 | 238.55 | 10−3 | 103.90 | ||
10−4 | 2,464.4 | 10−4 | 1155.5 | ||
10−5 | 24,888 | 10−5 | 12067 | ||
n = 0.5 | 10−2 | 12.854 | n = 1.5 | 10−2 | 3.9373 |
10−3 | 159.14 | 10−3 | 66.535 | ||
10−4 | 1,699.3 | 10−4 | 775.55 | ||
10−5 | 17,408 | 10−5 | 8288.2 |
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Khaled, A.-R.A.; Vafai, K. Analysis of Detection Enhancement Using Microcantilevers with Long-Slit-Based Sensors. Sensors 2013, 13, 681-702. https://doi.org/10.3390/s130100681
Khaled A-RA, Vafai K. Analysis of Detection Enhancement Using Microcantilevers with Long-Slit-Based Sensors. Sensors. 2013; 13(1):681-702. https://doi.org/10.3390/s130100681
Chicago/Turabian StyleKhaled, Abdul-Rahim A., and Kambiz Vafai. 2013. "Analysis of Detection Enhancement Using Microcantilevers with Long-Slit-Based Sensors" Sensors 13, no. 1: 681-702. https://doi.org/10.3390/s130100681
APA StyleKhaled, A.-R. A., & Vafai, K. (2013). Analysis of Detection Enhancement Using Microcantilevers with Long-Slit-Based Sensors. Sensors, 13(1), 681-702. https://doi.org/10.3390/s130100681