In this study, the structural vibration analysis and design of a Timoshenko beam with the attached tuned-mass-damper (TMD) under the harmonic and random excitations are presented using the finite element technique. A design optimization methodology has been developed in which the derived finite element formulation of a Timoshenko beam with the attached TMD has been combined with the sequential quadratic programming optimization algorithm to find the optimal design variables of TMD in order to suppress the vibration effectively. The validity of the developed optimal TMD system design strategy has been verified through illustrative examples, in which the structural response comparisons and the sensitivity analysis of the design parameters have been presented. The results were compared with those available in literatures and very close agreement was achieved.

Issue Section:
Research Papers
Keywords:
finite element analysis, quadratic programming, vibration control, vibrations, vibration suppression, Timoshenko beam, optimization, tuned-mass-damper (TMD), finite element method (FEM)
Topics:
Damping, Design, Optimization, Dampers, Finite element analysis, Finite element methods, Vibration, Vibration suppression, Random excitation
1.
Frahm
,
H.
, 1911, “
Device for Damping Vibration of Bodies
,” U.S. Patent No. 989,958.
2.
Den Hartog
,
J. P.
, 1956,
Mechanical Vibrations
, 4th ed.,
McGraw-Hill
,
New York
.
3.
Crandall
,
S. H.
, and
Mark
,
W. D.
, 1963,
Random Vibration in Mechanical Systems
,
Academic
,
New York
.
4.
Warburton
,
G. B.
, and
Ayorinde
,
E. O.
, 1980, “
Optimum Absorbers for Simple Systems
,”
Earthquake Eng. Struct. Dyn.
0098-8847,
8
(
3
), pp.
197
–
217
.
Crossref
Search ADS
 
5.
Warburton
,
G. B.
, 1982, “
Optimum Absorber Parameters for Various Combinations of Response and Excitation Parameters
,”
Earthquake Eng. Struct. Dyn.
0098-8847,
10
(
3
), pp.
381
–
401
.
Crossref
Search ADS
 
6.
Rana
,
R.
, and
Soong
,
T. T.
, 1998, “
Parametric Study and Simplified Design of Tuned Mass Damper
,”
Eng. Struct.
0141-0296,
20
(
3
), pp.
193
–
204
.
Crossref
Search ADS
 
7.
Li
,
H. N.
, and
Ni
,
X. L.
, 2007, “
Optimization of Non-Uniformly Distributed Multiple Tuned Mass Damper
,”
J. Sound Vib.
,
308
, pp.
80
–
97
. 0022-460X
Crossref
Search ADS
 
8.
Zuo
,
L.
, and
Nayfeh
,
S. A.
, 2005, “
Optimization of the Individual Stiffness and Damping Parameters in Multiple Tuned Mass Damper Systems
,”
ASME J. Vibr. Acoust.
0739-3717,
127
, pp.
77
–
83
.
Crossref
Search ADS
 
9.
Li
,
C.
, and
Zhu
,
B.
, 2006, “
Estimating Double Tuned Mass Dampers for Structures Under Ground Acceleration Using a Novel Optimum Criterion
,”
J. Sound Vib.
,
298
, pp.
280
–
297
. 0022-460X
Crossref
Search ADS
 
10.
Nishimura
,
I.
,
Yamada
,
T.
,
Sakamoto
,
M.
, and
Kobori
,
T.
, 1998, “
Control Performance of Active-Passive Composite Tuned Mass Damper
,”
Smart Mater. Struct.
,
7
, pp.
637
–
653
. 0964-1726
Crossref
Search ADS
 
11.
Esmailzadeh
,
E.
, and
Jalili
,
N.
, 1998, “
Optimal Design of Vibration Absorbers for Structurally Damped Timoshenko Beams
,”
ASME J. Vibr. Acoust.
0739-3717,
120
, pp.
833
–
841
.
Crossref
Search ADS
 
12.
Chen
,
T. H.
, and
Huang
,
Y. H.
, 2004, “
Timoshenko Beam With Tuned Mass Dampers and Its Design Curves
,”
J. Sound Vib.
0022-460X,
278
, pp.
873
–
888
.
Crossref
Search ADS
 
13.
Younesian
,
D.
,
Esmailzadeh
,
E.
, and
Sedaghati
,
R.
, 2006, “
Passive Vibration Control of Beams Subjected to Random Excitations With Peaked PSD
,”
J. Vib. Control
1077-5463,
12
(
9
), pp.
941
–
953
.
Crossref
Search ADS
 
14.
Lutes
,
L. D.
, and
Sarkani
,
S.
, 2004,
Random Vibration: Analysis of Structural and Mechanical Systems
,
Elsevier
,
Boston
.
15.
Rao
,
S. S.
, 1996,
Engineering Optimization: Theory and Practice
,
Wiley
,
New York
.
Copyright © 2009
 by American Society of Mechanical Engineers
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