Vibration suppression of a strain gradient Euler–Bernoulli beam in presence of disturbance and uncertainties is considered in this investigation. Vibration of the system is suppressed by an adaptive boundary controller which has robustness to the environmental and control effort disturbances. The direct Lyapunov stability theorem is used to design the controller and adaptation law. The numerical results are presented to demonstrate the effectiveness of the proposed controller.

References

1.
Lun
,
F.
,
Zhang
,
P.
,
Gao
,
F.
, and
Jia
,
H.
,
2006
, “
Design and Fabrication of Micro-Optomechanical Vibration Sensor
,”
Microfab. Technol.
,
120
(
1
), pp.
61
64
.
2.
Batra
,
R. C.
,
Porfiri
,
M.
, and
Spinello
,
D.
,
2008
, “
Vibrations of Narrow Microbeams Predeformed by an Electric Field
,”
J. Sound Vib.
,
309
(
3–5
), pp.
600
612
.
3.
Fleck
,
N. A.
,
Muller
,
G. M.
,
Ashby
,
M. F.
, and
Hutchinson
,
J. W.
,
1994
, “
Strain Gradient Plasticity: Theory and Experiment
,”
Acta Metall. Mater.
,
42
(
2
), pp.
475
487
.
4.
Ma
,
Q.
, and
Clarke
,
D. R.
,
1995
, “
Size Dependent Hardness of Silver Single Crystals
,”
J. Mater. Res.
,
10
(
4
), pp.
853
863
.
5.
Lam
,
D. C. C.
,
Yang
,
F.
,
Chong
,
A. C. M.
,
Wang
,
J.
, and
Tong
,
P.
,
2003
, “
Experiments and Theory in Strain Gradient Elasticity
,”
J. Mech. Phys. Solids
,
51
(
8
), pp.
1477
1508
.
6.
Kong
,
S.
,
Zhou
,
S.
,
Nie
,
Z.
, and
Wang
,
K.
,
2009
, “
Static and Dynamic Analysis of Micro Beams Based on Strain Gradient Elasticity Theory
,”
Int. J. Eng. Sci.
,
47
(
4
), pp.
487
498
.
7.
Zhao
,
J.
,
Zhou
,
S.
,
Wang
,
B.
, and
Wang
,
X.
,
2012
, “
Nonlinear Microbeam Model Based on Strain Gradient Theory
,”
Appl. Math. Model.
,
36
(
6
), pp.
2674
2686
.
8.
Vatankhah
,
R.
,
Kahrobaiyan
,
M. H.
,
Alasty
,
A.
, and
Ahmadian
,
M. T.
,
2013
, “
Nonlinear Forced Vibration of Strain Gradient Microbeams
,”
Appl. Math. Model.
,
37
(
18
), pp.
8363
8382
.
9.
Vatankhah
,
R.
,
Najafi
,
A.
,
Salarieh
,
H.
, and
Alasty
,
A.
,
2014
, “
Exact Boundary Controllability of Vibrating Non-Classical Euler–Bernoulli Micro-Scale Beams
,”
J. Math. Anal. Appl.
,
418
(
2
), pp.
985
997
.
10.
Vatankhah
,
R.
,
Najafi
,
A.
,
Salarieh
,
H.
, and
Alasty
,
A.
,
2014
, “
Asymptotic Decay Rate of Non-Classical Strain Gradient Timoshenko Micro-Cantilevers by Boundary Feedback
,”
J. Mech. Sci. Technol.
,
28
(
2
), pp.
627
635
.
11.
Meirovitch
,
L.
, and
Baruh
,
H.
,
1983
, “
On the Problem of Observation Spillover in Self-Adjoint Distributed-Parameter Systems
,”
J. Optim. Theory Appl.
,
39
(
2
), pp.
269
291
.
12.
Vatankhah
,
R.
,
Karami
,
F.
,
Salarieh
,
H.
, and
Alasty
,
A.
,
2013
, “
Stabilization of a Vibrating Non-Classical Micro-Cantilever Using Electrostatic Actuation
,”
Sci. Iran.: Trans. B, Mech. Eng.
,
20
(
6
), pp.
1824
1831
.
13.
Shahruz
,
S.
, and
Krishna
,
L.
,
1996
, “
Boundary Control of a Non-Linear String
,”
J. Sound Vib.
,
195
(
1
), pp.
169
174
.
14.
Baicu
,
C.
,
Rahn
,
C.
, and
Nibali
,
B.
,
1996
, “
Active Boundary Control of Elastic Cables: Theory and Experiment
,”
J. Sound Vib.
,
198
(
1
), pp.
17
26
.
15.
Fung
,
R.-F.
, and
Tseng
,
C.-C.
,
1999
, “
Boundary Control of an Axially Moving String Via Lyapunov Method
,”
ASME J. Dyn. Syst. Meas. Control
,
121
(
1
), pp.
105
110
.
16.
Ge
,
S. S.
,
He
,
W.
,
How
,
B. V. E.
, and
Choo
,
Y. S.
,
2010
, “
Boundary Control of a Coupled Nonlinear Flexible Marine Riser
,”
IEEE Trans. Control Syst. Technol.
,
18
(
5
), pp.
1080
1091
.
17.
He
,
W.
,
Ge
,
S. S.
,
How
,
B. V. E.
,
Choo
,
Y. S.
, and
Hong
,
K.-S.
,
2011
, “
Robust Adaptive Boundary Control of a Flexible Marine Riser With Vessel Dynamics
,”
Automatica
,
47
(
4
), pp.
722
732
.
18.
Hardy
,
G. H.
,
Littlewood
,
J. E.
, and
Polya
,
G.
,
1952
,
Inequalities
,
Cambridge University Press
,
Cambridge, London/New York
.
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