Undamped oscillators are often used to attenuate and control excess vibration in elastic structures. In this paper, vibration absorbers are used to impose nodes, i.e., points of zero vibration, along an arbitrarily supported linear structure externally forced by multiple steady-state harmonic excitations. An efficient approach is proposed to tune the absorber parameters based on the active force method. Using the active force approach, the oscillators are first replaced with the unknown restoring forces they exert. These restoring forces are found by enforcing the required node locations, and they correspond to the solution of a set of linear algebraic equations, which can be obtained using Gauss elimination. These restoring forces are subsequently used to tune the sprung masses. Because of the computational efficiency of the proposed method, design plots can be easily generated, from which specific sets of oscillator parameters can be selected. Even if the input consists of multiple frequencies, it is possible to induce multiple nodes anywhere on the structure by attaching properly tuned spring–mass oscillators. An efficient procedure to tune the oscillator parameters necessary to impose nodes at the desired locations is outlined in detail, and numerical case studies are presented to verify the utility of the proposed scheme to impose multiple nodes along an arbitrarily supported elastic structure subjected to external excitations consisting of multiple harmonics.

References

References
1.
Jacquot
,
R. G.
,
1978
, “
Optimal Dynamic Vibration Absorbers for General Beam Systems
,”
J. Sound Vib.
,
60
(
4
), pp.
535
542
.10.1016/S0022-460X(78)80090-X
2.
Özgüven
,
H. N.
, and
Çandir
,
B.
,
1986
, “
Suppressing the First and Second Resonances of Beams by Dynamic Vibration Absorbers
,”
J. Sound Vib.
,
111
(
3
), pp.
377
390
.10.1016/S0022-460X(86)81399-2
3.
Manikanahally
,
D. N.
, and
Crocker
,
M. J.
,
1991
, “
Vibration Absorbers for Hysterically Damped Mass-Loaded Beams
,”
ASME J. Vib. Acoust.
,
113
(
1
), pp.
116
122
.10.1115/1.2930145
4.
Keltie
,
R. F.
, and
Cheng
,
C. C.
,
1995
, “
Vibration Reduction of a Mass-Loaded Beam
,”
J. Sound Vib.
,
187
(
2
), pp.
213
228
.10.1006/jsvi.1995.0516
5.
Patten
,
W. N.
,
Sack
,
R. L.
, and
He
,
Q.
,
1996
, “
Controlled Semiactive Hydraulic Vibration Absorber for Bridges
,”
J. Struct. Eng.
,
122
(
2
), pp.
187
192
.10.1061/(ASCE)0733-9445(1996)122:2(187)
6.
Lee-Glauser
,
G. J.
,
Ahmadi
,
G.
, and
Horta
,
L. G.
,
1997
, “
Integrated Passive/Active Vibration Absorber for Multistory Buildings
,”
J. Struct. Eng.
,
123
(
4
), pp.
499
504
.10.1061/(ASCE)0733-9445(1997)123:4(499)
7.
Nagaya
,
K.
, and
Li
,
L.
,
1997
, “
Control of Sound Noise Radiated From a Plate Using Dynamic Absorbers Under the Optimization by Neural Network
,”
J. Sound Vib.
,
208
(
2
), pp.
289
298
.10.1006/jsvi.1997.1201
8.
Nagaya
,
K.
,
Kurusu
,
A.
,
Ikai
,
S.
, and
Shitani
,
Y.
,
1999
, “
Vibration Control of a Structure by Using a Tunable Absorber and an Optimal Vibration Absorber Under Auto-Tuning Control
,”
J. Sound Vib.
,
228
(
4
), pp.
773
792
.10.1006/jsvi.1999.2443
9.
Jacquot
,
R. G.
,
2001
, “
Suppression of Random Vibration in Plates Using Vibration Absorbers
,”
J. Sound Vib.
,
248
(
4
), pp.
585
596
.10.1006/jsvi.2001.3558
10.
Alsuwaiyan
,
A. S.
, and
Shaw
,
S. W.
,
2002
, “
Performance and Dynamic Stability of General-Path Centrifugal Pendulum Vibration Absorbers
,”
J. Sound Vib.
,
252
(
5
), pp.
791
815
.10.1006/jsvi.2000.3534
11.
Alsaif
,
K.
, and
Foda
,
M. A.
,
2002
, “
Vibration Suppression of a Beam Structure by Intermediate Masses and Springs
,”
J. Sound Vib.
,
256
(
4
), pp.
629
645
.10.1006/jsvi.2002.5012
12.
Dayou
,
J.
, and
Brennan
,
M. J.
,
2002
, “
Global Control of Structural Vibration Using Multiple-Tuned Tunable Vibration Neutralizers
,”
J. Sound Vib.
,
258
(
2
), pp.
345
357
.10.1006/jsvi.2002.5188
13.
Bhatta
,
P.
, and
Sinha
,
A.
,
2003
, “
A Discrete-Time, Optimal, Active Vibration Absorber
,”
J. Sound Vib.
,
268
(
1
), pp.
201
208
.10.1016/S0022-460X(03)00250-5
14.
Wong
,
W. O.
,
Tang
,
S. L
,
Cheung
,
Y. L.
, and
Cheng
,
L.
,
2006
, “
Design of a Dynamic Vibration Absorber for Vibration Isolation of Beams Under Point or Distributed Loading
,”
J. Sound Vib.
,
301
(
3–5
), pp.
898
908
.10.1016/j.jsv.2006.10.028
15.
Jacquot
,
R. G.
, and
Foster
,
J. E.
,
1977
, “
Optimal Cantilever Dynamic Vibration Absorbers
,”
ASME J. Manuf. Sci. Eng.
,
99
(
1
), pp.
138
141
.10.1115/1.3439127
16.
Cha
,
P. D.
,
2005
, “
Enforcing Nodes at Required Locations in a Harmonically Excited Structure Using Simple Oscillators
,”
J. Sound Vib.
,
279
(
3–5
), pp.
799
816
.10.1016/j.jsv.2003.11.067
17.
Cha
,
P. D.
, and
Ren
,
G.
,
2006
, “
Inverse Problem of Imposing Nodes to Suppress Vibration for a Structure Subjected to Multiple Harmonic Excitations
,”
J. Sound Vib.
,
290
(
1–2
), pp.
425
447
.10.1016/j.jsv.2005.04.025
18.
Cha
,
P. D.
, and
Chan
,
M.
,
2009
, “
Mitigating Vibration Along an Arbitrarily Supported Elastic Structure Using Multiple Two Degree-of-Freedom Oscillators
,”
ASME J. Vib. Acoust.
,
131
(
3
), p.
031008
.10.1115/1.3085891
19.
Abé
,
M.
, and
Igusa
,
T.
,
1996
, “
Semi-Active Dynamic Vibration Absorbers for Controlling Transient Response
,”
J. Sound Vib.
,
198
(
5
), pp.
547
569
.10.1006/jsvi.1996.0588
20.
Meirovitch
,
L.
,
2001
,
Fundamentals of Vibrations
,
McGraw-Hill
,
New York
.
21.
Gonçalves
,
P. J. P.
,
Brennan
,
M. J.
, and
Elliott
,
S. J.
,
2007
, “
Numerical Evaluation of Higher-Order Modes of Vibration in Uniform, Euler–Bernoulli Beams
,”
J. Sound Vib.
,
301
(
3–5
), pp.
1035
1039
.10.1016/j.jsv.2006.10.012
22.
Dowell
,
E. H.
,
1979
, “
On Some General Properties of Combined Dynamical Systems
,”
ASME J. Appl. Mech.
,
46
(
1
), pp.
206
209
.10.1115/1.3424499
You do not currently have access to this content.