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.
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Technical Brief
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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