Contributed by the Technical Committee on Vibration and Sound for publication in the JOURNAL OF VIBRATION AND ACOUSTICS. Manuscript received July 2001; Revised April 2002. Associate Editor: B. Yang.

Vibrations can be described as a linear combination of the modes of a structure 1. An alternative is to describe vibrations as propagating waves travelling in the structure. It was found that the two descriptions often give enlightening complementary perspectives 2,3.

Wave control can be feedforward 4. It can also be feedback. There exist two types of feedback wave control, namely the noncollocated and the collocated feedback wave control.

Longitudinally vibrating rod (or equivalently, transversely vibrating string) is studied in this Technical Brief. Though the classical modal approach can be used to analyze and control the vibrations in such structures 1,5, a spillover problem exists due to...

1.
Meirovitch, L., 1989, Dynamics and Control of Structures, John Wiley & Sons.
2.
Mei, C., 1998, “Hybrid Active Vibration Control of a Distributed System,” Ph.D. Thesis, The University of Auckland, Auckland, New Zealand.
3.
Pan
,
J.
, and
Pan
,
J.
,
1998
, “
A Comparison of Modal Expansion and Travelling Wave Methods for Predicting Energy Flow in Beam Structures
,”
J. Sound Vib.
,
214
(
1
), pp.
1
15
.
4.
Fuller, C. R., Elliot, S. J., and Nelson, P. A., 1996, Active Control of Vibration, Academic Press Ltd., San Diego, USA.
5.
Inman D. J., 1994, Engineering Vibration, Prentice-Hall International, Inc., USA.
6.
Nagem
,
R. J.
, and
Williams
, Jr.,
J. H.
,
1990
, “
Control of a One-Dimensional Distributed Structure Based on Wave Propagation Analysis
,”
Mech. Struct. Mach.
,
18
(
1
), pp.
33
57
.
7.
Chung
,
C. H.
, and
Tan
,
A. A.
,
1995
, “
Active Vibration Control of the Axially Moving String by Wave Cancellation
,”
ASME J. Vibr. Acoust.
,
117
, pp.
49
55
.
8.
Tan
,
C. A.
, and
Ying
,
S.
,
2000
, “
Active Wave Control of the Axially Moving String: Theory and Experiment
,”
J. Sound Vib.
,
236
(
5
), pp.
861
880
.
9.
Elliot, S. J., Brennan, M. J., and Pinnington, R. J., 1993, “Feedback Control of Flexural Waves on a Beam,” Proceedings of Inter-Noise 93, Leuven, Belgium, pp. 843–846.
10.
Mace
,
B. R.
, and
Jones
,
R. W.
,
1996
, “
Feedback Control of Flexural Waves in Beams
,”
Journal of Structural Control
,
3
(
1–2
), pp.
89
98
.
11.
Mei, C., Mace, B. R., and Jones, R. W., 1997, “Active Control of Flexural Vibrations Using Hybrid Mode/Wave Approach,” Proceedings of the Fifth International Congress on Sound and Vibration, Adelaide, Australia, pp. 437–444.
12.
Mei, C., Mace, B. R., and Jones, R. W., 1998, “Experimental Implementation of Hybrid Active Vibration Control of a Cantilever Beam,” Proceedings of Inter-noise 98, the 1998 International Congress on Noise Control Engineering, Christchurch, New Zealand.
13.
Lu
,
J.
,
Crocker
,
M. J.
, and
Raju
,
P. K.
,
1989
, “
Active Vibration Control Using Wave Control Concepts
,”
J. Sound Vib.
,
134
(
2
), pp.
364
368
.
14.
Lee
,
S. Y.
, and
Mote
, Jr.,
C. D.
,
1996
, “
Vibration Control of an Axially Moving String by Boundary Control
,”
ASME J. Dyn. Syst., Meas., Control
,
118
, pp.
66
74
.
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
, pp.
105
110
.
16.
Lee
,
S. Y.
, and
Mote
, Jr.,
C. D.
,
1998
, “
Travelling Wave Dynamics in a Translating String Coupled to Stationary Constraints: Energy Transfer and Mode Localization
,”
J. Sound Vib.
,
212
(
1
), pp.
1
22
.
17.
Hull
,
A. J.
,
1994
, “
A Closed Form Solution of A Longitudinal Bar With A Viscous Boundary Condition
,”
J. Sound Vib.
,
169
(
1
), pp.
19
28
.
18.
Thomson, W. T., 1989, Theory of Vibration with Applications, Unwin Hyman Ltd.
19.
Cremer, L., Heckel, M., and Ungar, E. E., 1988, Structure-Borne Sound, Berlin: Springer.
20.
Mace
,
B. R.
,
1984
, “
Wave Reflection and Transmission in Beams
,”
J. Sound Vib.
,
97
(
2
), pp.
237
246
.
21.
Mead
,
D. J.
,
1994
, “
Waves and Modes in Finite Beams: Application of the Phase-Closure Principle
,”
J. Sound Vib.
,
171
(
5
), pp.
695
702
.
22.
Mace
,
B. R.
,
1987
, “
Active Control of Flexural Vibrations
,”
J. Sound Vib.
,
114
(
2
), pp.
253
270
.
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