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188
Structural Model of a Nano Drive for Biomedical
Science
Copyright© Afonin SM
This work is licensed under Creative Commons Attribution 4.0 License
AJBSR.MS.ID.002825
.
American Journal of
Biomedical Science & Research
www.biomedgrid.com
---------------------------------------------------------------------------------------------------------------------------------
ISSN: 2642-1747
Research Article
Afonin SM*
National Research University of Electronic Technology, Russia
*Corresponding author: Afonin SM, National Research University of Electronic Technology, Russia.
To Cite This Article: Afonin SM*, Structural Model of a Nano Drive for Biomedical Sciencec. Am J Biomed Sci & Res. 2024 21(2) AJBSR.
MS.ID.002825, DOI: 10.34297/AJBSR.2024.21.002825
Received: : November 2, 2023; Published: January 23, 2024
Abstract
The structural model of a nano drive is determined for biomedical science. The structural scheme of the piezo drive is obtained. The matrix
equation is constructed for a nano drive.
Keywords: Nano drive, Piezo drive, Structural model and scheme, Matrix equation, Biomedical science
Introduction
A nano drive based on the piezomagnetic, magnetostriction,
piezoelectric, electrostriction effects is used for biomedical science,
nanomedicine, nanotechnology, nanobiology, microsurgery. The
piezo drive is used in scanning microscopy, astronomy for alignment
and focusing, image stabilization, in adaptive optics and work with
the genes [1-9]
Structural Model
The expression of electromagnet elasticity [1-15] has the forn
,EH H E
i ij j mi m mi m
S s T dE dH= ++
here
j
T
- the mechanical stress,
m
E
m
H
,EH
ij
s
- the elastic compliance for
const=E
,
const=H
,
H
mi
d
- the piezo module, E
mi
d- the magneto-
i
S
- the relative deformation, the axis i, j, m.
Therefore, the expression of the reverse piezo effect [1-15]
E
i mi m ij j
S d E sT= +
and the expression of the magneto strictive effect [1-15]
H
i mi m ij j
S d H sT= +
The expression of the shift inverses piezo effect [1-15]
5 15 1 55 5
E
S dE sT
= +
The differential equation of a nano drive is calculated [4-58]
( ) ( )
2
2
2
,,0
d xs xs
dx
γ
Ξ−Ξ =
here
( )
s,xΞ
,
x
, s,
γ
are the transform of displacement, the
For the shif piezo drive at
0=x
( ) ( )
ss,
1
0Ξ=Ξ
and at
xb=
( ) ( )
2
,bs sΞ=Ξ
and the solution of this differential equation is calcu-
lated
( ) ( ) ( ) ( ) ( )
{ }
( )
12
, sh sh shxs s b x s x b
γ γγ
Ξ = Ξ − +Ξ
At
0=x
and
bx =
the expressions [11-39] are written
( ) ( ) ( )
15
51
55 55
0
,
1
0, EE
x
d xs d
T s Es
s dx s
=
Ξ
= −
( ) ( ) ( )
15
51
55 55
,
1
,EE
xb
d xs d
T bs E s
s dx s
=
Ξ
= −
The structural model
( )
( )
( )
( )
( ) ( )
( ) ( ) ( )
1
1 55
1
2
11 15 1
12
sh
ch
E
Fs
s Ms dE s b
bs s
χ
γγ
γ
−
−
−+
Ξ=
−
×
× Ξ −Ξ
( )
( )
( )
( )
( ) ( )
( ) ( ) ( )
1
2 55
1
2
22 15 1
21
sh
ch
E
Fs
s Ms dEs b
bs s
χ
γγ
γ
−
−
−+
Ξ=
−
×
× Ξ −Ξ
Am J Biomed Sci & Res
American Journal of Biomedical Science & Research
Copyright© Afonin SM
189
189
55 55 0
EE
sS
χ
=
The expression of the shift magnetostrictive effect [1-15]
5 15 1 55 5
H
S dH sT= +
The structural model is transformed
( )
( )
( )
( )
( ) ( )
( ) ( ) ( )
1
1 55
1
2
11 15 1
12
sh
ch
H
Fs
s Ms dH s b
bs s
χ
γγ
γ
−
−
−+
Ξ=
−
×
× Ξ −Ξ
( )
( )
( )
( )
( ) ( )
( ) ( ) ( )
1
2 55
1
2
22 15 1
21
sh
ch
H
Fs
s Ms dH s b
bs s
χ
γγ
γ
−
−
−+
Ξ=
−
×
× Ξ −Ξ
55 55 0
HH
sS
χ
=
The expression of the transverse inverse piezo effect [1-15]
1 31 3 11 1
E
S d E sT= +
The solution is calculated
( ) ( ) ( ) ( ) ( )
{ }
( )
12
, sh sh shxs s h x s x h
γ γγ
Ξ = Ξ − +Ξ
The system at
0=x
and
hx =
is calculated
( )
( )
( )
31
13
11 11
0
,
1
0,
EE
x
d xs
d
T s Es
s dx s
=
Ξ
= −
( ) ( ) ( )
31
13
11 11
,
1
,EE
xh
d xs d
T hs E s
s dx s
=
Ξ
= −
The structural model has the form
( )
( )
( )
( )
( ) ( )
( ) ( ) ( )
1
1 11
1
2
11 31 3
12
sh
ch
E
Fs
s Ms dE s h
hs s
χ
γγ
γ
−
−
−+
Ξ=
−
×
× Ξ −Ξ
( )
( )
( )
( )
( ) ( )
( ) ( ) ( )
1
2 11
1
2
22 31 3
21
sh
ch
E
Fs
s Ms dE s h
hs s
χ
γγ
γ
−
−
−+
Ξ=
−
×
× Ξ −Ξ
11 11 0
EE
sS
χ
=
The expression of the transverse magneto strictive effect [1-15]
1 31 3 11 1
H
S dH sT= +
The structural model is transformed
( )
( )
( )
( )
( ) ( )
( ) ( ) ( )
1
1 11
1
2
11 31 3
12
sh
ch
H
Fs
s Ms dH s h
hs s
χ
γγ
γ
−
−
−+
Ξ=
−
×
× Ξ −Ξ
( )
( )
( )
( )
( ) ( )
( ) ( ) ( )
1
2 11
1
2
22 31 3
21
sh
ch
H
Fs
s Ms dH s h
hs s
χ
γγ
γ
−
−
−+
Ξ=
−
×
× Ξ −Ξ
11 11 0
HH
sS
χ
=
In general at
{
b,h,l δ=
the solution is calculated
( ) ( ) ( ) ( ) ( )
{ }
( )
12
, sh sh shxs s l x s x l
γ γγ
Ξ = Ξ − +Ξ
The system is transformed
( ) ( ) ( )
0
,
1
0, mi
jm
ij ij
x
d xs
Ts s
s dx s
ν
ΨΨ
=
Ξ
= −Ψ
( ) ( ) ( )
,
1
,mi
jm
ij ij
xl
d xs
T ls s
s dx s
ν
ΨΨ
=
Ξ
= −Ψ
The structural model on Figure 1 is calculated
( )
( )
( )
( )
( ) ( )
( ) ( ) ( )
1
1
1
2
11
12
sh
ch
ij
mi m
Fs
s Ms sl
ls s
χ
ν γγ
γ
−
Ψ
−
−+
Ξ=
Ψ−
×
× Ξ −Ξ
( )
( )
( )
( )
( ) ( )
( ) ( ) ( )
1
2
1
2
22
21
sh
ch
ij
mi m
Fs
s Ms
sl
lss
χ
ν γγ
γ
−
Ψ
−
−+
Ξ=
Ψ−
×
× Ξ −Ξ
0ij ij
sS
χ
ΨΨ
=
33 31 15
33 31 15
33 31 15
,,
,,
,,
mi
ddd
v ggg
ddd
=
=Ψ
13
13
13
,
,
,
HH
DD
EE
m
33 11 55
33 11 55
33 11 55
,,
,,
,,
EEE
DDD
ij
HHH
sss
s sss
sss
Ψ
=
{
HDE ,, γγγ=γ
{
HDE c,c,cc =
Ψ
The matrix of deformations is calculated (Figure 1)
( )
( )
( ) ( ) ( )
( ) ( ) ( )
( )
( )
( )
1 11 12 13
1
2 21 22 23
2
ms
s WsWsWs Fs
s WsWsWs Fs
Ψ
Ξ
=
Ξ
( ) ( ) ( ) ( )
2
11 1 2
th 2
m mi ij ij
Ws s s M s l A
ν χ γγ
Ψ
=ΞΨ= +
( )
( ) ( )
{ }
( ) ( )
( )
243
12 1 2
222
12
th
th 1 2
ij ij ij
ij
A MM s M M c l s
M M l c s sc
χ χγ
χα γ α α
Ψ ΨΨ
Ψ ΨΨ
= ++ +
++ + + +
( ) ( ) ( ) ( )
2
21 2 1 th 2
m mi ij ij
Ws s s M s l A
ν χ γγ
Ψ
=Ξ Ψ= +
( ) ( ) ( ) ( )
2
12 1 1 2 th
ij ij ij
W s s Fs M s l A
χ χγγ
ΨΨ
=Ξ=− +
( ) ( ) ( )
( ) ( ) ( ) ( )
13 1 2
22 2 1 sh
ij ij
W s sFs
W s s Fs l A
χγ γ
Ψ
=Ξ=
==Ξ=
( ) ( ) ( ) ( )
2
23 2 2 1
th
ij ij ij
W s s Fs M s l A
χ χγγ
ΨΨ
=Ξ=− +
In static the longitudinal deformations
American Journal of Biomedical Science & Research
Am J Biomed Sci & Res Copyright© Afonin SM
190
( )
1332 1 2
d UM M M
ξ
= +
( )
2 33 1 1 2
d UM M M
ξ
= +
For
33
d
= 410-10 m/V,
U
= 75 V,
1
M
= 1 kg,
2
M
= 4 kg the
static deformations
1
ξ
= 24 nm, 2
ξ
= 6 nm and 21
ξ+ξ
= 30 nm are
calculated at error 10%.
The expression of the direct piezo effect has form [1-15]
E
m mi i mk k
D dT E
ε
= +
here
m
D
- the electric induction,
E
mk
ε
- the permittivity.
The transform for the back electromotive force on Figure 2 is
evaluated
( ) ( ) ( )
0mi
dd
nn
E
ij
d SR
U s s kR s
s
δ
••
= Ξ=Ξ
,
21,n =
(Figure 2)
0mi
rd
ij
dS
kk s
δ
= =
Figure 1: Scheme of nano drive.
Figure 2: Scheme of piezo drive.
At voltage control of the piezo drive its characteristis are
evaluated
max
E
j m mi ij
T Ed s=
max 0
E
m mi ij
F Ed S s=
At current control of the piezo drive
0 max 0
max
0
11
mi mi c mi
E TE
ij mk c ij
SF S
U
F d dS d
sS S s
δ ε δδ
= +
2
max
0
1E
mi
ij m mi
TE
mk ij
Fd
s Ed
Ss
ε
−=
Am J Biomed Sci & Res
American Journal of Biomedical Science & Research
Copyright© Afonin SM
191
( )
2
max 1E
j mi ij m mi
T k s Ed
−=
ET
mi mi ij mk
kd s
ε
=
max
D
j m mi ij
T Ed s=
max 0
D
m mi ij
F Ed S s=
( )
2
1
DE
ij mi ij
s ks= −
here
c
S
- the sectional area of the capacitor,
0
C
- the capaci-
tance,
mi
k
For a nano drive the mechanical and adjustment characteristics
[11-26] are evaluated
const
const
i j mi m ij j
S T sT
ν
Ψ
Ψ=
Ψ= =Ψ+
()
const
const
i m mi m ij j
T
T
S sT
ν
Ψ
==
Ψ = Ψ+
The mechanical characteristic is written
( )
maxmax
1FFll −∆=∆
max mi m
ll
ν
∆=Ψ
max max 0 0j mi m ij
F T S Ss
ν
Ψ
= = Ψ
Therefore, for the transverse piezo drive this characteristic is
evaluated
( )
maxmax 1FFhh −∆=∆
max 31 3
h d Eh∆=
max 31 3 0 11
E
F d ES s=
At
31
d
-10 m/V,
3
E
5 V/m,
h
-2 m,
0
S
=
-5 m2,
11
E
s
-12 m2/N the values
max
h∆
= 750 nm and
max
F
= 30 N are found at error 10%
In static the deformation of a nano drive
0
ij e
mi m
sC
ll
lS
ν
Ψ
∆
= Ψ− ∆
lCF e∆=
The adjustment characteristic of a nano drive is evaluated
1
mi m
e ij
l
l
CC
ν
Ψ
Ψ
∆= +
here
E
ij s ij
s ks=
- the elastic compliance,
s
k
the change of elastic compliance
( )
2
11
mi s
kk− ≤≤
The expression for Figure 3 is evaluated
( ) ( ) ( ) ( )
sNksUssW r
=Ξ= 2
( )
32
2
1
3
0
asasasasN ++= +
0 02
a RC M=
,
12 0v
a M RC k= +
2 00v ij e r d
a k RC C RC C Rk k=+ ++
,
3e ij
a CC= +
here v
k
Figure 3: Scheme of piezo drive at one xed face.
At
0=R
the expression is evaluated
( )
( )
( )
31
22
21
U
t tt
sk
Ws U s Ts T s
ξ
Ξ
= =
++
( )
( )
31 31 11
1
UE
l
k d h CC
δ
= +
( )
11
E
tl
T MC C= +
,
tt T1=ω
+
For
M
= 4 kg, l
C
= 0.1107 N/m, 11
E
C
= 1.5107 N/m the values
t
T
= 0.510-3 s,
t
ω
= 2103 s-1 are calculated at error 10%.The static
deformation
()
31
31
11
1
U
E
l
dh U
h kU
CC
δ
∆= =
+
For
31
d
-10 m/V,
δh
= 22,
11
E
l
CC
31
U
k
= 4 nm/V is determined at error 10%.
Conclusion
For a nano drive the structural model is evaluated. The matrix
of the deformations is constructed. The characteristics of the piezo
drive are determined for biomedical science.
American Journal of Biomedical Science & Research
Am J Biomed Sci & Res Copyright© Afonin SM
192
Acknowledgement
None.
None.
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