In general, it is not possible to obtain total motion absorption of a certain degree of freedom in a harmonically excited damped system by passive control. This paper presents a method of obtaining total absorption in viscously damped system by active control, including time delay, which is unavoidable in digital controlled system. The control is applied on one degree of freedom and the absorption is achieved at another point. This study is carried out by both complex and real analyses. The necessary and sufficient condition for obtaining total absorption is given. Examples demonstrate the various results.

1.
den Hartog
,
J. P.
, 1947,
Mechanical Vibrations
, 3rd ed.,
McGraw-Hill
,
New York
.
2.
Cha
,
P. D.
, 2005, “
Enforcing Nodes at Required Locations in a Harmonically Excited Structure Using Simple Oscillators
,”
J. Sound Vib.
0022-460X,
279
, pp.
799
816
.
3.
Lee
,
E. C.
,
Nian
,
C. Y.
, and
Tarng
,
Y. S.
, 2001, “
Design of Dynamic Vibration Absorber Against Vibrations in Turning Operations
,”
J. Mater. Process. Technol.
0924-0136,
108
, pp.
278
285
.
4.
Song
,
Y.
,
Sato
,
H.
,
Iwata
,
Y.
, and
Komatsuzaki
,
T.
, 2003, “
The Response of a Dynamic Vibration Absorber System With a Parametrically Excited Pendulum
,”
J. Sound Vib.
0022-460X,
259
, pp.
747
759
.
5.
Yamashita
,
S.
,
Seto
,
K.
, and
Hara
,
F.
, 1989, “
Vibration Control In Piping System by Dual Dynamic Absorber (3-Dimensional Vibration Analysis and Absorber Design Using Transfer-Matrix Method)
,”
JSME Int. J., Ser. III
0914-8825,
32
, pp.
531
537
.
6.
Mottershead
,
J. E.
, and
Lallement
,
G.
, 1999, “
Vibration Nodes, and the Cancellations of Poles and Zeros by Unit-Rank Modifications to Structures
,”
J. Sound Vib.
0022-460X,
222
, pp.
833
851
.
7.
Mottershead
,
J. E.
, 2001, “
Structural Modification for the Assignment of Zeros Using Measured Receptances
,”
ASME J. Appl. Mech.
0021-8936,
68
, pp.
791
798
.
8.
Mottershead
,
J. E.
, 1998, “
On the Zeros of Structural Frequency Response Functions and Their Sensitivities
,”
Mech. Syst. Signal Process.
0888-3270,
12
, pp.
591
597
.
9.
Ram
,
Y. M.
, and
Elhay
,
S.
, 1996, “
The Theory of a Multi Degree of Freedom Dynamic Absorber
,”
J. Sound Vib.
0022-460X,
195
, pp.
607
615
.
10.
Ram
,
Y. M.
, 2002, “
Nodal Control of a Vibrating Rod
,”
Mech. Syst. Signal Process.
0888-3270,
16
, pp.
69
81
.
11.
Singh
,
K. V.
, and
Ram
,
Y. M.
, 2000, “
Dynamic Absorption by Passive and Active Control
,”
ASME J. Vibr. Acoust.
0739-3717,
122
, pp.
429
433
.
You do not currently have access to this content.