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Nanosensors
book

Nanosensors

by Vinod Kumar Khanna
April 2016
Intermediate to advanced content levelIntermediate to advanced
666 pages
22h 57m
English
CRC Press
Content preview from Nanosensors
239Mechanical Nanosensors
The values for β
i
are given in Table 4.1. From Equations 4.22 and 4.21, the
natural resonant frequency and its harmonics (frequencies that are integral
multiples of the fundamental frequency) are calculated:
ω
β
ρ
i
z
i
l
EI
A
=
2
2
(4.30)
For i = 1, β
i
2
= 3.516; and for a rectangular cantilever
I
wt
z
=
3
12
(4.31)
Hence from Equation 4.30, we get
ω
ρ ρ
1
=
=
3 516
12
1 015
2
3
2
.
.
l
Ewt
tw
E t
l
(4.32)
The fundamental frequency ω
1
is a function of the material parameters
E and ρ as well as the beam dimensions t and l. High frequencies are
achieved by reducing the overall cantilever scale, by choosing st ...
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Publisher Resources

ISBN: 9781439827130