Acoustic radiation from cylindrical shells stiffened by two sets of rings, with constrained layer damping (CLD), is investigated theoretically. The governing equations of motion for the cylindrical shell with CLD are described on the basis of Sanders thin shell theory. Two sets of rings interact with the host cylindrical shell only through the normal line forces. The solutions are derived in the wavenumber domain and the stationary phase method is used to find an analytical expression of the far-field sound pressure. The effects of the viscoelastic material core, constrained layer and multiple loadings on sound pressure are illustrated. The helical wave spectra of sound pressure and the radial displacement clearly show the vibrational and acoustic characteristics of the stiffened cylindrical shell with CLD. It is shown that CLD can effectively suppress the radial vibration and reduce acoustic radiation.

References

1.
Plunkett
,
R.
, and
Lee
,
C. T.
,
1970
, “
Length Optimization of Constrained Viscoelastic Layer Damping
,”
J. Acoust. Soc. Am.
,
48
(
2
), pp.
150
161
.10.1121/1.1912112
2.
Daneshjou
,
K.
,
Nouri
,
A.
, and
Talebitooti
,
R.
,
2008
, “
Analytical Model of Sound Transmission Through Laminated Composite Cylindrical Shells Considering Transverse Shear Deformation
,”
Appl. Math. Mech.
,
29
(
9
), pp.
1165
1177
.10.1007/s10483-008-0906-x
3.
Daneshjou
,
K.
,
Nouri
,
A.
, and
Talebitooti
,
R.
,
2009
, “
Analytical Model of Sound Transmission Through Orthotropic Cylindrical Shells With Subsonic External Flow
,”
Aerosp. Sci. Technol.
,
13
(
1
), pp.
18
26
.10.1016/j.ast.2008.02.005
4.
Yin
,
X. W.
,
Cui
,
H. F.
, and
Shen
,
S. G.
,
2009
, “
Acoustic Radiation From Two Concentric Cylindrical Shells With Periodic Supports and a Viscoelastic Perforated Outer Coating
,”
Acta Acust. Acust.
,
95
(
5
), pp.
823
832
.10.3813/AAA.918213
5.
Burroughs
,
C. B.
,
1984
, “
Acoustic Radiation From Fluid-Loaded Infinite Circular Cylinders With Doubly Periodic Ring Supports
,”
J. Acoust. Soc. Am.
,
75
(
3
), pp.
715
722
.10.1121/1.390582
6.
Mace
,
B. R.
,
1980
, “
Sound Radiation From a Plate Reinforced by Two Sets of Parallel Stiffeners
,”
J. Sound Vib.
,
71
(
3
), pp.
435
441
.10.1016/0022-460X(80)90425-3
7.
Mead
,
D. J.
, and
Markus
,
S.
,
1969
, “
The Forced Vibration of a Three-Layer, Damped Sandwich Beam With Arbitrary Boundary Conditions
,”
J. Sound Vib.
,
10
(
2
), pp.
163
175
.10.1016/0022-460X(69)90193-X
8.
Chen
,
Y. C.
, and
Huang
,
S. C.
,
2002
, “
An Optimal Placement of CLD Treatment for Vibration Suppression of Plates
,”
Int. J. Mech. Sci.
,
44
(
8
), pp.
1801
1821
.10.1016/S0020-7403(02)00042-5
9.
Gao
,
J. X.
, and
Shen
Y. P.
,
1999
, “
Vibration and Damping Analysis of a Composite Plate With Active and Passive Damping Layer
,”
Appl. Math. Mech.
,
20
(
10
), pp.
1075
1086
.10.1007/BF02460324
10.
Chen
,
L. H.
, and
Huang
,
S. C.
,
1999
, “
Vibrations of a Cylindrical Shell With Partially Constrained Layer Damping (CLD) Treatment
,”
Int. J. Mech. Sci.
,
41
(
12
), pp.
1485
1498
.10.1016/S0020-7403(98)00102-7
11.
Xiang
,
Y.
,
Huang
,
Y. Y.
,
Lu
,
J.
,
Yuan
,
L. Y.
, and
Zou
,
S. Z.
,
2008
, “
New Matrix Method for Analyzing Vibration and Damping Effect of Sandwich Circular Cylindrical Shell With Viscoelastic Core
,”
Appl, Math. Mech.
,
29
(
12
), pp.
1587
1600
.10.1007/s10483-008-1207-x
12.
Cao
,
X. T.
,
Zhang
,
Z. Y.
, and
Hua
,
H. X.
,
2011
, “
Free Vibration of Circular Cylindrical Shell With Constrained Layer Damping
,”
Appl. Math. Mech.
,
32
(
4
), pp.
495
506
.10.1007/s10483-011-1433-7
13.
Rao
,
D. K.
,
1978
, “
Frequency and Loss Factors of Sandwich Beams Under Various Boundary Conditions
,”
Int. J. Mech. Eng. Sci.
,
20
(
5
), pp.
271
282
.10.1243/JMES_JOUR_1978_020_047_02
14.
Lall
,
A. K.
,
Asnani
,
N. T.
, and
Nakra
,
B. C.
,
1988
, “
Damping Analysis of Partially Covered Sandwich Beams
,”
J. Sound Vib.
,
123
(
2
), pp.
247
259
.10.1016/S0022-460X(88)80109-3
15.
Kung
,
S. W.
, and
Singh
,
R.
,
1998
, “
Vibration Analysis of Beams With Multiple Constrained Layer Damping Patches
,”
J. Sound Vib.
,
212
(
5
), pp.
781
805
.10.1006/jsvi.1997.1409
16.
Zheng
,
H.
,
Tan
,
X. M.
, and
Cai
,
C.
,
2006
, “
Damping Analysis of Beams Covered With Multiple PCLD Patches
,”
Int. J. Mech. Sci.
,
48
(
12
), pp.
1371
1383
.10.1016/j.ijmecsci.2006.07.008
17.
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
(
3–5
), pp.
549
567
.10.1016/S0022-460X(03)00041-5
18.
McTavish
,
D. J.
, and
Hughes
,
P. C.
,
1993
, “
Modeling of Linear Viscoelastic Space Structures
,”
ASME J. Vibr. Acoust.
,
115
(
1
), pp.
103
110
.10.1115/1.2930302
19.
Golla
,
D. F.
, and
Hughes
,
P. C.
,
1985
, “
Dynamics of Viscoelastic Structures—A Time-Domain, Finite Element Formulation
,”
ASME J. Appl. Mech.
,
52
(
4
), pp.
897
906
.10.1115/1.3169166
20.
Lesieutre
,
G. A.
, and
Bianchini
,
E.
,
1995
, “
Time Domain Modeling of Linear Viscoelasticity Using Anelastic Displacement Fields
,”
ASME J. Vibr. Acoust.
,
117
(
4
), pp.
424
430
.10.1115/1.2874474
21.
Enelund
,
M.
, and
Lesieutre
,
G. A.
,
1999
, “
Time Domain Modeling of Damping Using Anelastic Displacement Fields and Fractional Calculus
,”
Int. J. Solids Struct.
,
36
(
29
), pp.
4447
4472
.10.1016/S0020-7683(98)00194-2
22.
Lesieutre
,
G. A.
, and
Lee
,
U.
,
1996
, “
A Finite Element For Beams Having Segmented Active Constrained Layers With Frequency-Dependent Viscoelastics
,”
Smart Mater. Struct.
,
5
(
5
), pp.
615
627
.10.1088/0964-1726/5/5/010
23.
Trindade
,
M. A.
,
Benjeddou
,
A.
, and
Ohayon
,
R.
,
2000
, “
Modeling of Frequency-Dependent Viscoelastic Materials for Active-Passive Vibration Damping
,”
ASME J. Vibr. Acoust.
,
122
(
2
), pp.
169
174
.10.1115/1.568429
24.
Trindade
,
M. A.
,
2006
, “
Reduced-Order Finite Element Models of Viscoelastically Damped Beams Through Internal Variables Projection
,”
ASME J. Vibr. Acoust.
,
128
(
4
), pp.
501
508
.10.1115/1.2202155
25.
Liu
,
T.
,
Hua
,
H. X.
, and
Zhang
,
Z. Y.
,
2004
, “
Robust Control of Plate Vibration via Active Constrained Layer Damping
,”
Thin-Walled Struct.
,
42
(
3
), pp.
427
448
.10.1016/S0263-8231(03)00131-9
26.
Panda
,
S.
, and
Ray
,
M. C.
,
2009
, “
Control of Nonlinear Vibrations of Functionally Graded Plates Using 1-3 Piezoelectric Composite
,”
AIAA J.
,
47
(
6
), pp.
1421
1434
.10.2514/1.38048
27.
Panda
,
S.
, and
Ray
,
M. C.
,
2009
, “
Active Control of Geometrically Nonlinear Vibrations of Functionally Graded Laminated Composite Plates Using Piezoelectric Fiber Reinforced Composites
,”
J. Sound Vib.
,
325
(
1–2
), pp.
186
205
.10.1016/j.jsv.2009.03.016
28.
Li
,
S.
, and
Zhao
,
D.
,
2004
, “
Numerical Simulation of Active Control of Structural Vibration and Acoustic Radiation of a Fluid-Loaded Laminated Plate
,”
J. Sound Vib.
,
272
(
1–2
), pp.
109
124
.10.1016/S0022-460X(03)00321-3
29.
Ray
,
M. C.
,
Faye
,
A.
,
Patra
,
S.
, and
Bhattacharyya
,
R.
,
2009
, “
Theoretical and Experimental Investigations on the Active Structural-Acoustic Control of a Thin Plate Using a Vertically Reinforced 1-3 Piezoelectric Composite
,”
Smart Mater. Struct.
,
18
(
1
), p.
015012
.10.1088/0964-1726/18/1/015012
30.
Assaf
,
S.
,
Guerich
,
M.
, and
Cuvelier
,
P.
,
2010
, “
Vibration and Acoustic Response of Damped Sandwich Plates Immersed in a Light or Heavy Fluid
,”
Comput. Struct.
,
88
(
13–14
), pp.
870
878
.10.1016/j.compstruc.2010.04.006
31.
Ramesh
,
T. C.
, and
Ganesan
,
N.
,
1994
, “
Finite Element Analysis of Conical Shells With a Constrained Viscoelastic Layer
,”
J. Sound Vib.
,
171
(
5
), pp.
577
601
.10.1006/jsvi.1994.1143
32.
Ramesh
,
T. C.
, and
Ganesan
,
N.
,
1994
, “
Finite Element Analysis of Cylindrical Shells With a Constrained Viscoelastic Layer
,”
J. Sound Vib.
,
172
(
3
), pp.
359
370
.10.1006/jsvi.1994.1180
33.
Ramesh
,
T.C.
, and
Ganesan
,
N.
,
1994
, “
Orthotropic Cylindrical Shells With a Viscoelastic Core: A Vibration and Damping Analysis
,”
J. Sound Vib.
,
175
(
4
), pp.
535
555
.10.1006/jsvi.1994.1344
34.
Ray
,
M. C.
,
Oh
,
J.
, and
Baz
,
A.
,
2001
, “
Active Constrained Layer Damping of Thin Cylindrical Shells
,”
J. Sound Vib.
,
240
(
5
), pp.
921
935
.10.1006/jsvi.2000.3287
35.
Masti
,
R. S.
, and
Sainsbury
,
M. G.
,
2005
, “
Vibration Damping of Cylindrical Shells Partially Coated With a Constrained Viscoelastic Treatment Having a Standoff Layer
,”
Thin-Walled Struct.
,
43
(
9
), pp.
1355
1379
.10.1016/j.tws.2005.06.007
36.
Oh
,
I. K.
,
2007
, “
Dynamic Characteristics of Cylindrical Hybrid Panels Containing Viscoelastic Layer Based on Layerwise Mechanics
,”
Composites, Part B
38
(
2
), pp.
159
171
.10.1016/j.compositesb.2006.07.002
37.
Zheng
,
L.
,
Zhang
,
D. D.
, and
Wang
,
Y.
,
2011
, “
Vibration and Damping Characteristics of Cylindrical Shells With Active Constrained Layer Damping Treatments
,”
Smart Mater. Struct.
,
20
(
2
), p.
025008
.10.1088/0964-1726/20/2/025008
38.
Ruzzene
,
M.
, and
Baz
,
A.
,
2000
, “
Finite Element Modeling of Vibration and Sound Radiation From Fluid-Loaded Damped Shells
,”
Thin-Walled Struct.
,
36
(
1
), pp.
21
46
.10.1016/S0263-8231(99)00035-X
39.
Oh
,
J.
,
Ruzzene
,
M.
, and
Baz
,
A.
,
2002
, “
Passive Control of the Vibration and Sound Radiation From Submerged Shells
,”
J. Vib. Control
,
8
(
4
), pp.
425
449
.10.1177/107754602023689
40.
Laplante
,
W.
,
Chen
,
T. H.
,
Baz
,
A.
, and
Shields
,
W.
,
2002
, “
Active Control of Vibration and Noise Radiation From Fluid-Loaded Cylinder Using Active Constrained Layer Damping
,”
J. Vib. Control
,
8
(
6
), pp.
877
902
.10.1177/1077546029206
41.
Krishna
,
B. V.
, and
Ganesan
,
N.
,
2007
, “
Studies on Fluid-Filled and Submerged Cylindrical Shells With Constrained Viscoelastic Layer
,”
J. Sound Vib.
,
303
(
3–5
), pp.
575
595
.10.1016/j.jsv.2007.01.009
42.
Foin
,
O.
,
Nicolas
,
J.
, and
Atalla
,
N.
,
1999
, “
An Efficient Tool for Predicting the Structural Acoustic and Vibration Response of Sandwich Plates in Light or Heavy Fluid
,”
Appl. Acoust.
,
57
(
3
), pp.
213
242
.10.1016/S0003-682X(98)00059-0
43.
EI-Raheb
,
M.
, and
Wagner
,
P.
,
1986
, “
Damped Response of Shells by a Constrained Viscoelastic Layer
,”
ASME J. Appl. Mech.
,
53
(
4
), pp.
902
908
.10.1115/1.3171879
44.
Yuan
,
L.
,
Xiang
,
Y.
,
Huang
,
Y.
, and
Lu
,
J.
,
2010
, “
A Semi-Analytical Method and the Circumferential Dominant Modal Control of Circular Cylindrical Shells With Active Constrained Layer Damping Treatment
,”
Smart Mater. Struct.
,
19
(
2
), pp.
1
14
.10.1088/0964-1726/19/2/025010
45.
Lu
,
J.
,
Xiang
,
Y.
,
Huang
,
Y. Y.
,
Li
,
X. L.
, and
Ni
,
Q.
,
2010
, “
Transfer Matrix Method for Analyzing Vibration and Damping Characteristics of Rotational Shell With Passive Constrained Layer Damping Treatment
,”
Acta Mech. Solida Sinica
,
23
(
4
), pp.
297
311
.10.1007/s10338-010-1001-z
46.
Xiang
,
Y.
,
Yuan
,
L.
,
Huang
,
Y. Y.
, and
Ni
,
Q.
,
2011
, “
A Novel Matrix Method for Coupled Vibration and Damping Effect Analyses of Liquid-Filled Circular Cylindrical Shells With Partially Constrained Layer Damping Under Harmonic Excitation
,”
Appl. Math. Modell.
,
35
(
5
), pp.
2209
2220
.10.1016/j.apm.2010.11.018
47.
Chen
,
L. H.
, and
Huang
,
S. C.
,
2001
, “
Vibration Attenuation of a Cylindrical Shell With Constrained Layer Damping Strips Treatment
,”
Comput. Structures
,
79
(
14
), pp.
1355
1362
.10.1016/S0045-7949(01)00009-8
48.
Nilsson
,
A. C.
,
1990
, “
Wave Propagation in and Sound Transmission Through Sandwich Plates
,”
J. Sound Vib.
,
138
(
1
), pp.
73
94
.10.1016/0022-460X(90)90705-5
49.
Mead
,
D. J.
, and
Yaman
,
Y.
,
1991
, “
The Harmonic Response of Rectangular Sandwich Plates With Multiple Stiffening: A Flexural Wave Analysis
,”
J. Sound Vib.
,
145
(
3
), pp.
409
428
.10.1016/0022-460X(91)90111-V
50.
Park
,
C. H.
, and
Baz
,
A.
,
2004
, “
Newtonian and Variational Formulations of the Dynamics of Plates With Active Constrained Layer Damping Treatments
,”
J. Vib. Control
,
10
(
3
), pp.
399
421
.10.1177/1077546304033364
51.
Pan
,
H. H.
,
1969
, “
Axisymmetrical Vibrations of a Circular Sandwich Shell With a Viscoelastic Core Layer
,”
J. Sound Vib.
,
9
(
2
), pp.
338
348
.10.1016/0022-460X(69)90038-8
52.
Baz
,
A.
, and
Chen
,
T.
,
2000
, “
Control of Axi-Symmetric Vibrations of Cylindrical Shells Using Active Constrained Layer Damping
,”
Thin-Walled Struct.
,
36
(
1
), pp.
1
20
.10.1016/S0263-8231(99)00034-8
53.
Pan
,
X.
,
Tso
,
Y.
, and
Juniper
R.
,
2008
, “
Active Control of Radiated Pressure of a Submarine Hull
,”
J. Sound Vib.
,
311
(
1–2
), pp.
224
242
.10.1016/j.jsv.2007.09.001
54.
Caresta
,
M.
, and
Kessissoglou
N.
,
2012
, “
Active Control of Sound Radiated by a Submarine Hull in Axisymmetric Vibration Using Inertial Actuators
,”
ASME J. Vibr. Acoust.
,
134
(
1
), p.
011002
.10.1115/1.4004673
55.
Yin
,
X. W.
,
Liu
,
L. J.
,
Hua
,
H. X.
, and
Shen
,
R. Y.
,
2009
, “
Acoustic Radiation From an Infinite Laminated Composite Cylindrical Shell With Doubly Periodic Rings
,”
ASME J. Vibr. Acoust.
,
131
(
1
), p.
0110051
.10.1115/1.2980376
56.
Soedel
,
W.
,
1993
,
Vibrations of Shells and Plates
,
Marcel Dekker
,
New York
.
57.
Yan
,
J.
,
Li
,
T. Y.
,
Liu
,
T. G.
, and
Liu
,
J. X.
,
2006
, “
Characteristics of the Vibrational Power Flow Propagation in a Submerged Periodic Ring-Stiffened Cylindrical Shell
,”
Appl. Acoust.
,
67
(
6
), pp.
550
569
.10.1016/j.apacoust.2005.08.006
58.
Junger
,
M. C.
, and
Feit
,
D.
,
1986
,
Sound, Structures, and Their Interactions
,
MIT
,
Cambridge, MA
.
59.
Williams
,
E. G.
,
Houston
,
B. H.
, and
Bucaro
,
J. A.
,
1990
, “
Experimental Investigation of the Wave Propagation on a Pointdriven, Submerged Capped Cylinder Using k-Space Analysis
,”
J. Acoust. Soc. Am.
,
87
(
2
), pp.
513
522
.10.1121/1.398922
60.
Choi
,
S. H.
,
Igusa
,
T.
, and
Achenbach
,
J. D.
,
1995
, “
Nonaxisymmetric Vibration and Acoustic Radiation of a Submerged Cylindrical Shell of Finite Length Containing Internal Substructures
,”
J. Acoust. Soc. Am.
,
98
(
1
), pp.
353
362
.10.1121/1.413689
61.
Lin
,
T. R.
,
Mechefske
,
C.
, and
O'Shea
,
P.
,
2011
, “
Characteristics of Modal Sound Radiation of Finite Cylindrical Shells
,”
ASME J. Vibr. Acoust.
,
133
(
5
), p.
0510111
.10.1115/1.4003944
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