Abstract

This paper investigates the nonlinear dynamic behavior of a cantilever beam made of composite material without and with lumped mass fixed along its length. The analysis compares the results coming from analytical and numerical modeling with experimental observations. The first part focuses on the analytical model. The model takes into account the nonlinearity derived from large amplitude vibration and inertia. The second part deals with the experimental test, where the specimen and the data acquisition are defined. Then, the nonlinearity of the acquired data is determined by the fitting time history (FTH) technique. The third part deals with the finite element model. Finally, the results obtained by the analytical method, the experimental method, and the numerical method are compared between each other.

References

1.
Hinnant
,
H. E.
, and
Hodges
,
D. H.
,
1988
, “
Nonlinear Analysis of a Cantilever Beam
,”
AIAA J.
,
26
(
12
), pp.
1521
1537
.10.2514/3.10072
2.
Zavodney
,
L. D.
, and
Nayfeh
,
A. H.
,
1989
, “
The Non-Linear Response of a Slender Beam Carrying a Lumped Mass to a Principal Parametric Excitation: Theory and Experiment
,”
Int. J. Non-Linear Mech.
,
24
(
2
), pp.
105
125
.10.1016/0020-7462(89)90003-6
3.
Crespo da Silva
,
M. R. M.
, and
Glynn
,
C. C.
,
1978
, “
Nonlinear Flexural-Torsional Dynamics of Inextensional Beams—II: Forced Motions
,”
J. Struct. Mech.
,
6
(
4
), pp.
449
461
.10.1080/03601217808907349
4.
Awrejcewicz
,
J.
,
Krysko
,
A. V.
,
Soldatov
,
V.
, and
Krysko
,
V. A.
,
2012
, “
Analysis of the Nonlinear Dynamics of the Timoshenko Flexible Beams Using Wavelets
,”
ASME J. Comput. Nonlinear Dyn.
,
7
(
1
), p.
011005
.10.1115/1.4004376
5.
Eisley
,
J. G.
,
1964
, “
Nonlinear Deformation of Elastic Beams, Rings and Strings
,”
Wear
,
7
(
3
), pp.
225
312
.
6.
Beléndez
,
T.
,
Neipp
,
C.
, and
Beléndez
,
A.
,
2002
, “
Large and Small Deflections of a Cantilever Beam
,”
Eur. J. Phys.
,
23
(
3
), pp.
371
379
.10.1088/0143-0807/23/3/317
7.
Navaee
,
S.
, and
Elling
,
R. E.
,
1991
, “
Large Deflections of Cantilever Beams
,”
Trans. Can. Soc. Mech. Eng.
,
15
(
1
), pp.
91
107
.10.1139/tcsme-1991-0005
8.
Anderson
,
T. J.
,
Nayfeh
,
A. H.
, and
Balachandran
,
B.
,
1996
, “
Experimental Verification of the Importance of the Nonlinear Curvature in the Response of a Cantilever Beam
,”
ASME J. Vib. Acoust.
,
118
(
1
), pp.
21
27
.10.1115/1.2889630
9.
Babilio
,
E.
, and
Lenci
,
S.
,
2017
, “
On the Notion of Curvature and Its Mechanical Meaning in a Geometrically Exact Plane Beam Theory
,”
Int. J. Mech. Sci.
,
128–129
, pp.
277
293
.10.1016/j.ijmecsci.2017.03.031
10.
Zheng
,
Y.
,
Shabana
,
A. A.
, and
Zhang
,
D.
,
2018
, “
Curvature Expressions for the Large Displacement Analysis of Planar Beam Motions
,”
ASME J. Comput. Nonlinear Dyn.
,
13
(
1
), p.
011013
.10.1115/1.4037226
11.
Lenci
,
S.
,
Clementi
,
F.
, and
Rega
,
G.
,
2016
, “
A Comprehensive Analysis of Hardening/Softening Behavior of Shearable Planar Beams With Whatever Axial Boundary Constraint
,”
Meccanica
,
51
(
11
), pp.
2589
2606
.10.1007/s11012-016-0374-6
12.
Meesala
,
V. C.
, and
Hajj
,
M. R.
,
2019
, “
Response Variations of a Cantilever Beam–Tip Mass System With Nonlinear and Linearized Boundary Conditions
,”
J. Vib. Control
,
25
(
3
), pp.
485
496
.10.1177/1077546318809853
13.
Sedighi
,
H. M.
, and
Shirazi
,
K. H.
,
2012
, “
A New Approach to Analytical Solution of Cantilever Beam Vibration With Nonlinear Boundary Condition
,”
ASME J. Comput. Nonlinear Dyn.
,
7
(
3
), p.
034502
.10.1115/1.4005924
14.
McHugh
,
K. A.
, and
Dowell
,
E. H.
,
2019
, “
Nonlinear Response of an Inextensible, Cantilevered Beam Subjected to a Nonconservative Follower Force
,”
ASME J. Comput. Nonlinear Dyn.
,
14
(
3
), p.
031004
.10.1115/1.4042324
15.
Hamdan
,
M. N.
, and
Shabaneh
,
N. H.
,
1997
, “
On the Large Amplitude Free Vibrations of a Restrained Uniform Beam Carrying an Intermediate Lumped Mass
,”
J. Sound Vib.
,
199
(
5
), pp.
711
736
.10.1006/jsvi.1996.0672
16.
Hamdan
,
M. N.
, and
Dado
,
M. H. F.
,
1997
, “
Large Amplitude Free Vibrations of a Uniform Cantilever Beam Carrying an Intermediate Lumped Mass and Rotary Inertia
,”
J. Sound Vib.
,
206
(
2
), pp.
151
168
.10.1006/jsvi.1997.1081
17.
Wagner
,
H.
,
1965
, “
Large-Amplitude Free Vibrations of a Beam
,”
ASME J. Appl. Mech.
,
32
(
4
), pp.
887
892
.10.1115/1.3627331
18.
Wu
,
H. L.
,
Yang
,
J.
, and
Kitipornchai
,
S.
,
2016
, “
Nonlinear Vibration of Functionally Graded Carbon Nanotube-Reinforced Composite Beams With Geometric Imperfections
,”
Compos. Part B
,
90
(
1
), pp.
86
96
. 10.1016/j.compositesb.2015.12.007
19.
Ke
,
L.-L.
,
Yang
,
J.
, and
Kitipornchai
,
S.
,
2010
, “
Nonlinear Free Vibration of Functionally Graded Carbon Nanotube-Reinforced Composite Beams
,”
Compos. Struct.
,
92
(
3
), pp.
676
683
.10.1016/j.compstruct.2009.09.024
20.
Feng
,
C.
,
Yang
,
J.
, and
Kitipornchai
,
S.
,
2017
, “
Nonlinear Free Vibration of Functionally Graded Polymer Composite Beams Reinforced With Graphene Nanoplatelets (GPLS)
,”
Eng. Struct.
,
140
, pp.
110
119
.10.1016/j.engstruct.2017.02.052
21.
Lenci
,
S.
,
Consolini
,
L.
, and
Clementi
,
F.
,
2017
, “
The Use of the Fitting Time Histories Method to Detect the Nonlinear Behaviour of Laminated Glass
,”
J. Vib. Test. Syst. Dyn.
,
1
(
1
), pp.
1
14
.10.5890/JVTSD.2017.03.001
22.
Lenci
,
S.
,
Consolini
,
L.
,
Clementi
,
F.
, and
Cocchi
,
G.
,
2017
, “
Revealing Nonlinear Dynamical Behaviour of Laminated Glass
,”
Procedia Eng.
,
199
, pp.
1454
1459
.10.1016/j.proeng.2017.09.394
23.
Mahmoodi
,
S. N.
,
Jalili
,
N.
, and
Khadem
,
S. E.
,
2008
, “
An Experimental Investigation of Nonlinear Vibration and Frequency Response Analysis of Cantilever Viscoelastic Beams
,”
J. Sound Vib.
,
311
(
3–5
), pp.
1409
1419
.10.1016/j.jsv.2007.09.027
24.
Nayfeh
,
A. H.
,
2000
,
Perturbation Methods
,
Wiley
,
Hoboken, NJ
.
25.
Hijmissen
,
J. W.
, and
Van Horssen
,
W. T.
,
2007
, “
On Aspects of Damping for a Vertical Beam With a Tuned Mass Damper at the Top
,”
Nonlinear Dyn.
,
50
(
1–2
), pp.
169
190
.10.1007/s11071-006-9150-9
26.
Hijmissen
,
J. W.
, and
Van Horssen
,
W. T.
,
2008
, “
On the Weakly Damped Vibrations of a Vertical Beam With a Tip-Mass
,”
J. Sound Vib.
,
310
(
3
), pp.
740
754
.10.1016/j.jsv.2007.06.014
27.
Schwalbe
,
D.
, and
Wagon
,
S.
,
1997
,
The Duffing Equation
,
Wiley
,
Hoboken, NJ
.
28.
Liu
,
W. H.
, and
Huang
,
C. C.
,
1988
, “
Free Vibration of Restrained Beam Carrying Concentrated Masses
,”
J. Sound Vib.
,
123
(
1
), pp.
31
42
.10.1016/S0022-460X(88)80075-0
29.
Hamdan
,
M. N.
, and
Latif
,
L. A.
,
1994
, “
On the Numerical Convergence of Dicretization Methods for the Free Vibrations of Beams With Attached Intertia Elements
,”
J. Sound Vib.
,
169
(
4
), pp.
527
545
.10.1006/jsvi.1994.1032
30.
Gindy
,
M.
,
Vaccaro
,
R.
,
Nassifand
,
H.
, and
Velde
,
J.
,
2008
, “
A State-Space Approach for Deriving Bridge Displacement From Acceleration
,”
Comput.-Aided Civ. Inf.
,
23
(
4
), pp.
281
290
.10.1111/j.1467-8667.2007.00536.x
31.
Kropp
,
P. K.
,
1997
,
Experimental Study of the Dynamic Response of Highway Bridges
,
Joint Highway Research Project
,
West Lafayette, IN
.
You do not currently have access to this content.