Abstract

This paper is concerned with the analysis of the effectiveness of triangular shaped smart constrained layer damping (SCLD) treatment in attenuating geometrically nonlinear transient vibrations of laminated composite beams. The SCLD treatment is comprised of an advanced vertically reinforced 1–3 piezoelectric composite (PZC) as the constraining layer and an isotropic viscoelastic layer as the constrained layer, which is modeled using a two-dimensional fractional order derivative (FOD) model with Grünwald definition of the FODs. A nonlinear meshfree model of the smart composite beam is developed for analyzing its nonlinear transient response within the framework of a layerwise shear and normal deformation theory considering von Kármán type geometric nonlinearity. Cantilever type composite beams having different lamination sequences integrated with regular rectangular/triangular type of SCLD treatments are considered for presenting the numerical results. For comparison purpose, a geometrical constraint has been imposed such that both the rectangular and triangular shaped SCLD treatments will cover the equal area on the top surface of the beam. The numerical analyses demonstrate the effectiveness of the triangular shaped SCLD patches over the rectangular SCLD treatment in controlling the nonlinear vibration of laminated composite beams. The two-dimensional FOD model of the viscoelastic material has been efficiently implemented for the active damping analysis of smart composite beam.

References

References
1.
Preumont
,
A.
,
2011
,
Vibration Control of Active Structures: An Introduction
, Vol.
179
,
Springer Science & Business Media
,
Springer, Berlin
.
2.
Datta
,
P.
, and
Ray
,
M. C.
,
2016
, “
Three-Dimensional Fractional Derivative Model of Smart Constrained Layer Damping Treatment for Composite Plates
,”
Compos. Struct.
,
156
, pp.
291
306
.10.1016/j.compstruct.2015.10.021
3.
Sahoo
,
S. R.
, and
Ray
,
M. C.
,
2018
, “
Analysis of Smart Damping of Laminated Composite Beams Using Mesh Free Method
,”
Int. J. Mech. Mater. Des.
,
14
(
3
), pp.
359
374
.10.1007/s10999-017-9379-0
4.
Kerwin
,
E. M.
, Jr
,
1959
, “
Damping of Flexural Waves by a Constrained Viscoelastic Layer
,”
J. Acoust. Society Am.
,
31
(
7
), pp.
952
962
.10.1121/1.1907821
5.
Bailey
,
T.
, and
Ubbard
,
J. E.
,
1985
, “
Distributed Piezoelectric-Polymer Active Vibration Control of a Cantilever Beam
,”
J. Guid., Control, Dyn.
,
8
(
5
), pp.
605
611
.10.2514/3.20029
6.
Plump
,
J. M.
,
Hubbard
,
J. E.
, and
Bailey
,
T.
,
1987
, “
Nonlinear Control of a Distributed System: Simulation and Experimental Results
,”
ASME J. Dyn. Syst., Meas., Control
,
109
(
2
), pp.
133
139
.10.1115/1.3143830
7.
Brunner
,
A. J.
,
Birchmeier
,
M.
,
Melnykowycz
,
M. M.
, and
Barbezat
,
M.
,
2009
, “
Piezoelectric Fiber Composites as Sensor Elements for Structural Health Monitoring and Adaptive Material Systems
,”
J. Intell. Mater. Syst. Struct.
,
20
(
9
), pp.
1045
1055
.10.1177/1045389X08101196
8.
Ray
,
M. C.
,
Bhattacharya
,
R.
, and
Samanta
,
B.
,
1993
, “
Exact Solutions for Static Analysis of Intelligent Structures
,”
AIAA J.
,
31
(
9
), pp.
1684
1691
.10.2514/3.11831
9.
Chandrashekhara
,
K.
, and
Agarwal
,
A. N.
,
1993
, “
Active Vibration Control of Laminated Composite Plates Using Piezoelectric Devices: A Finite Element Approach
,”
J. Intell. Mater. Syst. Struct.
,
4
(
4
), pp.
496
508
.10.1177/1045389X9300400409
10.
Ray
,
M. C.
, and
Pradhan
,
A. K.
,
2007
, “
On the Use of Vertically Reinforced 1-3 Piezoelectric Composites for Hybrid Damping of Laminated Composite Plates
,”
Mech. Adv. Mater. Struct.
,
14
(
4
), pp.
245
261
.10.1080/15376490600795683
11.
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
), p.
615
.10.1088/0964-1726/5/5/010
12.
Baz
,
A.
,
1997
, “
Boundary Control of Beams Using Active Constrained Layer Damping
,”
ASME J. Vib. Acoust.
,
119
(
2
), pp.
166
172
.10.1115/1.2889698
13.
Han
,
J. H.
,
Rew
,
K. H.
, and
Lee
,
I.
,
1997
, “
An Experimental Study of Active Vibration Control of Composite Structures With a Piezo-Ceramic Actuator and a Piezo-Film Sensor
,”
Smart Mater. Struct.
,
6
(
5
), p.
549
.10.1088/0964-1726/6/5/006
14.
Liao
,
W. H.
, and
Wang
,
K. W.
,
1997
, “
On the Analysis of Viscoelastic Materials for Active Constrained Layer Damping Treatments
,”
J. Sound Vib.
,
207
(
3
), pp.
319
334
.10.1006/jsvi.1997.1106
15.
Balamurugan
,
V.
, and
Narayanan
,
S.
,
2002
, “
Finite Element Formulation and Active Vibration Control Study on Beams Using Smart Constrained Layer Damping (SCLD) Treatment
,”
J. Sound Vib.
,
249
(
2
), pp.
227
250
.10.1006/jsvi.2001.3804
16.
Baz
,
A.
,
1998
, “
Robust Control of Active Constrained Layer Damping
,”
J. Sound Vib.
,
211
(
3
), pp.
467
480
.10.1006/jsvi.1997.1315
17.
Ko
,
S. H.
,
Park
,
C. H.
,
Park
,
H. C.
, and
Hwang
,
W.
,
2004
, “
Vibration Control of an Arc Type Shell Using Active Constrained Layer Damping
,”
Smart Mater. Struct.
,
13
(
2
), p.
350
.10.1088/0964-1726/13/2/013
18.
Sahoo
,
S. R.
, and
Ray
,
M. C.
,
2018
, “
Active Control of Laminated Composite Plates Using Elliptical Smart Constrained Layer Damping Treatment
,”
Compos. Struct.
,
211
, pp.
376
389
.10.1016/j.compstruct.2018.12.004
19.
Badre-Alam
,
A.
,
Wang
,
K. W.
, and
Gandhi
,
F.
,
1999
, “
Optimization of Enhanced Active Constrained Layer (EACL) Treatment on Helicopter Flexbeams for Aeromechanical Stability Augmentation
,”
Smart Mater. Struct.
,
8
(
2
), p.
182
.10.1088/0964-1726/8/2/003
20.
Liu
,
Q.
,
Chattopadhyay
,
A.
,
Gu
,
H.
,
Liu
,
Q.
,
Chattopadhyay
,
A.
, and
Zhou
,
X.
,
2000
, “
Use of Segmented Constrained Layer Damping Treatment for Improved Helicopter Aeromechanical Stability
,”
Smart Mater. Struct.
,
9
(
4
), p.
523
.10.1088/0964-1726/9/4/316
21.
Van Nostrand
,
W. C.
,
Knowles
,
G. J.
, and
Inman
,
D. J.
,
1993
, “
Active Constrained Layer Damping for Micro-Satellites
,”
Dynamics and Control of Structures in Space
, Southampton, UK, pp.
667
681
.
22.
Shields
,
W.
,
Ro
,
J.
, and
Baz
,
A.
,
1998
, “
Control of Sound Radiation From a Plate Into an Acoustic Cavity Using Active Piezoelectric-Damping Composites
,”
Smart Mater. Struct.
,
7
(
1
), p.
1
.10.1088/0964-1726/7/1/002
23.
Ray
,
M. C.
, and
Faye
,
A.
,
2009
, “
Active Structural-Acoustic Control of Laminated Composite Plates Using Vertically/Obliquely Reinforced 1–3 Piezoelectric Composite Patch
,”
Int. J. Mech. Mater. Des.
,
5
(
2
), p.
123
.10.1007/s10999-008-9089-8
24.
Biswas
,
D.
, and
Ray
,
M. C.
,
2013
, “
Active Constrained Layer Damping of Geometrically Nonlinear Vibration of Rotating Composite Beams Using 1-3 Piezoelectric Composite
,”
Int. J. Mech. Mater. Des.
,
9
(
1
), pp.
83
104
.10.1007/s10999-012-9207-5
25.
Panda
,
S.
, and
Ray
,
M. C.
,
2012
, “
Active Damping of Nonlinear Vibrations of Functionally Graded Laminated Composite Plates Using Vertically/Obliquely Reinforced 1-3 Piezoelectric Composite
,”
ASME J. Vib. Acoust.
,
134
(
2
), p.
021016
.10.1115/1.4004604
26.
Ray
,
M. C.
, and
Reddy
,
J. N.
,
2013
, “
Active Damping of Laminated Cylindrical Shells Conveying Fluid Using 1–3 Piezoelectric Composites
,”
Compos. Struct.
,
98
, pp.
261
271
.10.1016/j.compstruct.2012.09.051
27.
Zhang
,
D.
, and
Zheng
,
L.
,
2014
, “
Active Vibration Control of Plate Partly Treated With ACLD Using Hybrid Control
,”
Int. J. Aerosp. Eng.
,
2014
, p.
432970
.10.1155/2014/432970
28.
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
29.
McTavish
,
D. J.
, and
Hughes
,
P. C.
,
1993
, “
Modeling of Linear Viscoelastic Space Structures
,”
ASME J. Vib. Acoust.
,
115
(
1
), pp.
103
110
.10.1115/1.2930302
30.
Datta
,
P.
, and
Ray
,
M. C.
,
2018
, “
Smart Damping of Geometrically Nonlinear Vibrations of Composite Shells Using Fractional Order Derivative Viscoelastic Constitutive Relations
,”
Mech. Adv. Mater. Struct.
,
25
(
1
), pp.
62
78
.10.1080/15376494.2016.1255811
31.
Bagley
,
R. L.
, and
Torvik
,
J.
,
1983
, “
Fractional Calculus-a Different Approach to the Analysis of Viscoelastically Damped Structures
,”
AIAA J.
,
21
(
5
), pp.
741
748
.10.2514/3.8142
32.
Bagley
,
R. L.
, and
Torvik
,
P. J.
,
1985
, “
Fractional Calculus in the Transient Analysis of Viscoelastically Damped Structures
,”
AIAA J.
,
23
(
6
), pp.
918
925
.10.2514/3.9007
33.
Pritz
,
T.
,
1996
, “
Analysis of Four-Parameter Fractional Derivative Model of Real Solid Materials
,”
J. Sound Vib.
,
195
(
1
), pp.
103
115
.10.1006/jsvi.1996.0406
34.
Galucio
,
A. C.
,
Deü
,
J.-F.
, and
Ohayon
,
R.
,
2004
, “
Finite Element Formulation of Viscoelastic Sandwich Beams Using Fractional Derivative Operators
,”
Comput. Mech.
,
33
(
4
), pp.
282
291
.10.1007/s00466-003-0529-x
35.
Galucio
,
A. C.
,
Deu
,
J. F.
, and
Ohayon
,
R.
,
2005
, “
A Fractional Derivative Viscoelastic Model for Hybrid Active-Passive Damping Treatments in Time Domain-Application to Sandwich Beams
,”
J. Intell. Mater. Syst. Struct.
,
16
(
1
), pp.
33
45
.10.1177/1045389X05046685
36.
Sasso
,
M.
,
Palmieri
,
G.
, and
Amodio
,
D.
,
2011
, “
Application of Fractional Derivative Models in Linear Viscoelastic Problems
,”
Mech. Time-Depend. Mater.
,
15
(
4
), pp.
367
387
.10.1007/s11043-011-9153-x
37.
Eldred
,
L. B.
,
Baker
,
W. P.
, and
Palazotto
,
A. N.
,
1995
, “
Kelvin-Voigt Versus Fractional Derivative Model as Constitutive Relations for Viscoelastic Materials
,”
AIAA J.
,
33
(
3
), pp.
547
550
.10.2514/3.12471
38.
Reddy
,
J. N.
,
1997
,
Mechanics of Laminated Composite Plates: Theory and Analysis
,
CRC Press
,
Boca Raton, FL
.
39.
Zener
,
C. M.
, and
Siegel
,
S.
,
1949
, “
Elasticity and Anelasticity of Metals
,”
J. Phys. Chem.
,
53
(
9
), pp.
1468
1468
.10.1021/j150474a017
40.
Schmidt
,
A.
, and
Gaul
,
L.
,
2002
, “
Finite Element Formulation of Viscoelastic Constitutive Equations Using Fractional Time Derivatives
,”
Nonlinear Dyn.
,
29
(
1/4
), pp.
37
55
.10.1023/A:1016552503411
41.
Belytschko
,
T.
,
Lu
,
Y. Y.
, and
Gu
,
L.
,
1994
, “
Element-Free Galerkin Methods
,”
Int. J. Numer. Methods Eng.
,
37
(
2
), pp.
229
256
.10.1002/nme.1620370205
42.
Liu
,
G. R.
,
2009
,
Meshfree Methods: Moving Beyond the Finite Element Method
, CRC press, Boca Raton, FL.
43.
Krishnaswamy
,
S.
,
Chandrashekhara
,
K.
, and
Wu
,
W. Z. B.
,
1992
, “
Analytical Solutions to Vibration of Generally Layered Composite Beams
,”
J. Sound Vib.
,
159
(
1
), pp.
85
99
.10.1016/0022-460X(92)90452-4
44.
Kapania
,
R. K.
, and
Raciti
,
S.
,
1989
, “
Nonlinear Vibrations of Unsymmetrically Laminated Beams
,”
AIAA J.
,
27
(
2
), pp.
201
210
.10.2514/3.10082
45.
Bhashyam
,
G. R.
, and
Prathap
,
G.
,
1980
, “
Galerkin Finite Element Method for Non-Linear Beam Vibrations
,”
J. Sound Vib.
,
72
(
2
), pp.
191
203
.10.1016/0022-460X(80)90652-5
46.
Alnefaie
,
K.
,
2009
, “
Finite Element Modeling of Composite Plates With Internal Delamination
,”
Compos. Struct.
,
90
(
1
), pp.
21
27
.10.1016/j.compstruct.2009.01.004
47.
Reddy
,
J. N.
,
1983
, “
Geometrically Nonlinear Transient Analysis of Laminated Composite Plates
,”
AIAA J.
,
21
(
4
), pp.
621
629
.10.2514/3.8122
48.
Ogata
,
K.
, and
Yang
,
Y.
,
2002
,
Modern Control Engineering
, Vol.
4
,
Prentice Hall
,
Prentice Hall, London, UK
.
You do not currently have access to this content.