This work deals with the design and experimental evaluation of a passive/active cantilever beam autoparametric vibration absorber mounted on a two-story building-like structure (primary system), with two rigid floors connected by flexible columns. The autoparametric vibration absorber consists of a cantilever beam with a piezoelectric patch actuator, cemented to its base, mounted on the top of the structure and actively controlled through an acquisition system. The overall system is then a coupled nonlinear oscillator subjected to sinusoidal excitation in the neighborhood of its external and internal resonances. The addition of the piezoelectric patch actuator to the cantilever beam absorber makes active the passive vibration absorber, thus enabling the possibility to control its equivalent stiffness and damping and, as a consequence, the implementation of an active vibration control scheme able to preserve, as possible, the autoparametric interaction as well as to compensate varying excitation frequencies and parametric uncertainty.

References

1.
Spencer
,
B. F.
, Jr.
, and
Nagarajaiah
,
S.
,
2003
, “
State of the Art of Structural Control
,”
J. Struct. Eng.
,
129
(
7
), pp.
845
856
.10.1061/(ASCE)0733-9445(2003)129:7(845)
2.
Battaini
,
M.
,
Casciati
,
F.
, and
Faravelli
,
L.
,
1998
, “
Fuzzy Control of Structural Vibration. An Active Mass System Driven by a Fuzzy Controller
,”
Earthquake Eng. Struct. Dyn.
,
27
(
11
), pp.
1267
1276
.10.1002/(SICI)1096-9845(1998110)27:11%3C1267::AID-EQE782%3E3.0.CO
3.
Sun
,
J. Q.
,
Jolly
,
M. R.
, and
Norris
,
M. A.
,
1995
, “
Passive, Adaptive and Active Tuned Vibration Absorbers—A Survey
,”
ASME J. Vib. Acoust.
,
117
(
B
), pp.
234
242
.10.1115/1.2838668
4.
Korenev
,
B. G.
, and
Reznikov
,
L. M.
,
1993
,
Dynamic Vibration Absorber: Theory and Technical Applications
,
Wiley
,
London
, UK.
5.
Ibrahim
,
R. A.
, and
Heo
,
H.
,
1986
, “
Autoparametric Vibration of Coupled Beams Under Random Support Motion
,”
ASME J. Vib. Acoust.
,
108
(
4
), pp.
421
426
.10.1115/1.3269365
6.
Dahlberg
,
T.
,
1989
, “
On Optimal Use of the Mass of a Dynamic Vibration Absorber
,”
J. Sound Vib.
,
132
(
3
), pp.
518
522
.10.1016/0022-460X(89)90645-7
7.
Preumont
,
A.
,
2006
,
Mechatronics: Dynamics of Electromechanical and Piezoelectric Systems
,
Springer
,
Dordrecht, The Netherlands
.
8.
Song
,
G.
,
Sethi
,
V.
, and
Li
,
H. N.
,
2006
, “
Vibration Control of Civil Structures Using Piezoceramic Smart Materials: A Review
,”
Eng. Struct.
,
28
(11), pp.
1513
1524
.10.1016/j.engstruct.2006.02.002
9.
Haxton
,
R. S.
, and
Barr
,
A. D. S.
,
1972
, “
The Autoparametric Vibration Absorber
,”
J. Eng. Ind.
,
94
(
1
), pp.
119
124
.10.1115/1.3428100
10.
Cartmell
,
M. P.
,
1990
,
Introduction to Linear, Parametric and Nonlinear Vibrations
,
Chapman and Hall
,
London
, UK.
11.
Tondl
,
A.
,
Ruijgrok
,
T.
,
Verhulst
,
F.
, and
Nabergoj
,
R.
,
2000
,
Autoparametric Resonance in Mechanical Systems
,
Cambridge University Press
,
Cambridge, MA
.
12.
Nayfeh
,
A. H.
, and
Mook
,
D. T.
,
1979
,
Nonlinear Oscillations
,
Wiley
,
New York
.
13.
Roberts
,
J. W.
,
1980
, “
Random Excitation of a Vibratory System With Autoparametric Interaction
,”
J. Sound Vib.
,
69
(
1
), pp.
101
116
.10.1016/0022-460X(80)90437-X
14.
Cuvalci
,
O.
, and
Ertas
,
A.
,
1996
, “
Pendulum as Vibration Absorber for Flexible Structures: Experiments and Theory
,”
ASME J. Vib. Acoust.
,
118
(
4
), pp.
558
566
.10.1115/1.2888335
15.
Cuvalci
,
O.
,
Ertas
,
A.
,
Ekwaro-Osire
,
S.
, and
Cicek
,
I.
,
2002
, “
Non-Linear Vibration Absorber for a System Under Sinusoidal and Random Excitation: Experiments
,”
J. Sound Vib.
,
249
(
4
), pp.
701
718
.10.1006/jsvi.2001.3836
16.
Vazquez-Gonzalez
,
B.
, and
Silva-Navarro
,
G.
,
2008
, “
Evaluation of the Autoparametric Pendulum Vibration Absorber for a Duffing System
,”
Shock Vib.
,
15
(
3–4
), pp.
355
368
.10.1155/2008/827129
17.
Cartmell
,
M. P.
,
1990
, “
The Equations of Motion for a Parametrically Excited Cantilever Beam
,”
J. Sound Vib.
,
143
(
3
), pp.
395
406
.10.1016/0022-460X(90)90731-E
18.
Silva-Navarro
,
G.
,
Macias-Cundapi
,
L.
, and
Vazquez-Gonzalez
,
B.
,
2010
, “
Design of a Passive/Active Autoparametric Pendulum Absorber for Damped Duffing Systems
,”
New Trends in Electrical Engineering, Automatic Control, Computing and Communication Science
,
C. A.
Coello
,
A.
Pozniak
,
J. A.
Moreno
, and
V.
Azhmyakov
, eds.,
Logos-Verlag
,
Berlin, Germany
, pp.
159
175
.
19.
Abundis-Fong
,
H. F.
,
Silva-Navarro
,
G.
, and
Vazquez-Gonzalez
,
B.
,
2013
, “
Design of a Passive/Active Autoparametric Cantilever Beam Absorber With PZT Actuator for a Building-Like Structure
,”
ASME
Paper No. SMASIS2013-3230.10.1115/SMASIS2013-3230
20.
Chopra
,
A. K.
,
2001
,
Dynamics of Structures
,
Prentice-Hall
,
Englewood Cliffs, NJ
.
21.
Forehand
,
D. I. M.
, and
Cartmell
,
M. P.
,
2001
, “
On the Derivation of the Equations of Motion for a Parametrically Excited Cantilever Beam
,”
J. Sound Vib.
,
245
(
1
), pp.
165
177
.10.1006/jsvi.2000.3530
22.
Anderson
,
T. J.
,
Nayfeh
,
A. H.
, and
Balachandran
,
B.
,
1996
, “
Experimental Verification of the Importance of the Nonlinear Curvature in the Response of a Cantilever Beam
,”
ASME J. Vib. Acoust.
,
118
(
1
), pp.
21
27
.10.1115/1.2889630
23.
Gus’kov
,
A. M.
,
Panovko
,
G. Ya.
, and
Bin
,
C. V.
,
2008
, “
Analysis of the Dynamics of a Pendulum Vibration Absorber
,”
J. Mach. Manuf. Reliab.
,
37
(
4
), pp.
321
329
.10.3103/S105261880804002X
24.
Yabuno
,
H.
,
Endo
,
Y.
, and
Aoshima
,
N.
,
1999
, “
Stabilization of 1/3-Order Subharmonic Resonance Using an Autoparametric Vibration Absorber
,”
ASME J. Vib. Acoust.
,
121
(
3
), pp.
309
315
.10.1115/1.2893981
25.
Yabuno
,
H.
,
Murakami
,
T.
,
Kawazoe
,
J.
, and
Aoshima
,
N.
,
2004
, “
Suppression of Parametric Resonance in Cantilever Beam With a Pendulum (Effect of Static Friction at the Supporting Point of the Pendulum)
,”
ASME J. Vib. Acoust.
,
126
(
1
), pp.
149
162
.10.1115/1.1596554
26.
Craig
,
R. K.
, and
Kurdila
,
A. J.
,
2006
,
Fundamentals of Structural Dynamics
,
Wiley, Hoboken, NJ
.
27.
Domaneschi
,
M.
,
2012
, “
Simulation of Controlled Hysteresis by the Semi-Active Bouc-Wen Model
,”
Comput. Struct.
,
106–107
, pp.
245
257
.10.1016/j.compstruc.2012.05.008
You do not currently have access to this content.