For active/passive vibration control applications, low order models of flexible structures are always preferable. Mathematical models of passive constrained layer damping (PCLD)/active constrained layer damping (ACLD) treatment generated by energy based analytical methods are of much smaller orders as compared to finite element methods (FEM). Using these analytical methods, one can get rid of complex model reduction techniques, since these model reduction techniques are subjected to errors if applied directly to PCLD or ACLD systems. However, analytical techniques cannot be applied blindly to any PCLD system. There is significant error in loss factor prediction for certain boundary conditions. This error is also dependent on the relative thicknesses of Viscoelastic material layer, constraining layer and base beam. For certain combination of the above thicknesses and under certain boundary conditions, the models generated are useless for controller design purposes. On the other hand, FEM are highly robust and can be applied easily to any set of boundary conditions with guaranteed accuracy. Also, results predicted by this method are of high accuracy for any combinations of thicknesses of different layers. The only disadvantage of this technique is the high order of the developed model. Detailed performance comparison of both the techniques to predict the modal parameters of the PCLD treated beam is presented.

References

References
1.
Rajiv
,
K.
,
Singh
,
S. P.
, and
Chandrawat
,
H. N.
, 2005, “
Multivariable Adaptive Vibration Control of Smart Structures Using Iterative LQG Control Strategies
,”
Smart Mater. Struct.
,
14
(
5
), pp.
953
962
.
2.
Rajiv
,
K.
,
Singh
,
S. P.
, and
Chandrawat
,
H. N.
, 2006, “
Optimized Near Minimum Time Control of Smart Structures Using Variable Gain LQG Control Strategies
,”
J. Vibr. Acoust.
,
128
(
3
), pp.
402
407
.
3.
Rajiv
,
K.
, and
Singh
,
S. P.
, 2006, “
Adaptive Hybrid Control of Smart Structures Subjected to Multiple Disturbances
,”
Smart Mater. Struct.
,
15
(
5
), pp.
1345
1357
.
4.
Rajiv
,
K.
,
Singh
,
S. P.
, and
Chandrawat
,
H. N.
, 2006, “
Adaptive Vibration Control of Smart Structures: A Comparative Study
,”
Smart Mater. Struct.
15
(
5
), pp.
1358
1369
.
5.
Rajiv
,
K.
, 2007, “
Pole Placement Techniques for Active Vibration Control of Smart Structures: A Feasibility Study
,”
J. Vibr. Acoust.
,
129
(
5
), pp.
601
615
.
6.
Rajiv
,
K.
,
Singh
,
S. P.
, and
Chandrawat
,
H.N.
, 2007, “
MIMO Adaptive Vibration Control of Smart Structures with Quickly Varying Parameters: Neural Networks vs Classical Control Approach
,”
J. Sound. Vib.
,
307
, pp.
639
661
.
7.
Swallow
,
W.
, 1939, “
An Improved Method of Damping Panel Vibrations
,”
British Patent Specification 513
.
8.
Kervin
,
E. M.
, 1959, “
Damping of Flexural Waves by a Constrained Visco-elastic Layer
,”
J. Acoust. Soc. Am.
,
31
, pp.
952
962
.
9.
Ross
,
D.
,
Ungar
,
E.
, and
Kervin
,
E. M.
,
Damping of Plate Flexural Vibrations by Means of Viscoelastic Laminae, Structural Damping
(
ASME
,
New York
, 1959).
10.
Di Taranto
,
R. A.
, 1965, “
Theory of Vibratory Bending for Elastic and Viscoelastic Finite Length Beams
,”
ASME Trans. J. Appl. Mech.
32
, pp.
881
886
.
11.
Mead
,
D. J.
, and
Markus
,
S.
, 1969, “
The Force Vibration of a Three Layer Damped Sandwich Beam with Arbitrary Boundary Conditions
,”
J. Sound Vib.
,
10
, pp.
163
175
.
12.
Yan
,
M. J.
, and
Dowell
,
E. H.
, 1972, “
Governing Equations for Vibrating Constrained Layer Damping of Sandwich Beams and Plates
,
ASME Trans. J. Appl. Mech.
,
94
, pp.
1041
1047
.
13.
Mead
,
D. J.
, 1982, “
A Comparison of Some Equations for the Flexural Vibration of Damped Sandwich Beams
,”
J. Sound Vib.
,
83
(
3
), pp.
363
377
.
14.
Huang
,
S. C.
,
Inman
,
D. J.
, and
Austin
,
E. M.
, 1996, “
Some Design Considerations for Active and Passive Constrained Layer Damping Treatments
,”
Smart Mater Struct.
,
5
, pp.
301
313
.
15.
Nokes
,
D. S.
, and
Nelson
,
F. C.
, 1968, “
Constrained Layer Damping with Partial Coverage
,”
Shock and Vibration Bulletin
,
38
, pp.
5
10
.
16.
Lall
,
A. K.
,
Ansari
,
N. T.
, and
Nackra
,
B. C.
, 1988, “
Damping Analysis of Partially Covered Sandwich Beams
,”
J. Sound Vib.
,
123
(
2
), pp.
247
259
.
17.
Lall
,
A. K.
,
Ansari
,
N. T.
, and
Nackra
,
B. C.
, 1987, “
Vibration and Damping Analysis of Rectangular Plate with Partially Covered Constrained Viscoelastic Layer
,”
ASME J. Vib., Acoust., Stress, Reliab. Des.
,
109
, pp.
241
247
.
18.
Kung
,
S. W.
, and
Singh
,
R.
, 1998, “
Vibration Analysis of Beams with Multiple Constrained Layer Damping Patches
,”
J. Sound Vib.
,
121
(
5
), pp.
781
805
.
19.
Fasana
,
A.
, and
Marchesiello
,
S.
, 2001, “
Rayleigh – Ritz Analysis of Sandwich Beams
,”
J. Sound Vib.
,
241
(
4
), pp.
643
652
.
20.
Gao
,
J.
, and
Shen
,
Y.
, 1999, “
Dynamic Characteristic of a Cantilever Beam with Partial Self Sensing Active Constrained Layer Damping Treatment
,”
Acta Mech. Solida Sinica
,
12
(
4
), pp.
316
327
.
21.
Sainsbury
,
M. G.
, and
Zhang
,
Q. J.
, 1999, “
The Galerkin Element Method Applied to the Vibration of Damped Sandwich Beams
,”
Comput. Struct.
,
71
, pp.
239
256
.
22.
Liu
,
Y.
, and
Wang
,
K. W.
, 2000, “
Active – Passive Hybrid Constrained Layer for Structural Damping Augmentation
,”
ASME J. Vibr. Acoust.
122
, pp.
254
262
.
23.
Oh
,
J.
,
Poh
,
S.
,
Ruzzene
,
M.
, and
Baz
,
A.
, 2000, “
Vibration Control of Beams Using Electromagnetic Compressional Damping Treatment
,
ASME J. Vibr. Acoust.
122
, pp.
235
243
.
24.
Hau
,
L. C.
, and
Fung
,
E. H. K.
, 2004, “
Effect of ACLD Treatment Configuration on Damping Performance of a Flexible Beam
,”
J. Sound. Vib.
,
269
, pp.
549
567
.
25.
Shi
,
Y.
,
Hua
,
H.
, and
Sol
,
H
, 2004, “
The Finite Element Analysis and Experimental Study of Beams with Active Constrained Layer Damping Treatments
,”
J. Sound Vib.
,
278
, pp.
343
363
.
26.
Park
,
C. H.
,
Inman
,
D. J.
, and
Lam
,
M. J.
, 1999, “
Model Reduction of Viscoelastic Finite Element Models
,”
J. Sound Vib.
219
, pp.
619
637
.
27.
Friswell
,
M. I.
,
Garvey
,
S. D.
, and
Penny
,
J. E. T.
, 1995, “
Model Reduction Using Dynamic and Iterated IRD Techniques
,”
J. Sound Vib.
186
(
2
), pp.
311
323
.
28.
Rajiv
,
K.
, 2011, “
System Identification Based Model Reduction of Beams Treated with ACLD Treatment Part I: – Comparison with Existing Techniques
,”
J. Sound Vib.
(submitted).
29.
Cai
,
C.
,
Zheng
,
H.
, and
Liu
,
R
, 2004, “
Vibration Analysis of a Beam with PCLD Treatment
,”
Appl. Acoust.
,
65
(
11
), pp.
1057
1076
.
30.
Granger
,
D.
, and
Ross
,
A.
, 2008, “
Effects of Partial Constrained Viscoelastic Layer Damping Parameters on the Initial Transient Response of Impacted Cantilever Beams: Experimental and Numerical Results
,”
J. Sound Vib.
,
321
, pp.
45
64
.
You do not currently have access to this content.