Analytical investigations into dynamic properties of glued-laminated beams reinforced with various lay ups of e-glass reinforced epoxy polymer composites are discussed. The exp-function method is used to obtain generalized solitonary solutions and periodic solutions for nonlinear evolution equations arising in mathematical physics using symbolic computation. By using this method, natural frequency and dynamic responses of the wood-composite beams are obtained. The existing data obtained from our published work, the grindosonic instrument, and also the data from the beams tested using the power spectral density method is used for validity of analytical method. The data from finite element method as a numerical method was also employed. The comparison indicated that the proposed exp-function method could be effectively used to establish the natural frequency and dynamic properties of glulam reinforced composite beams when conducted in nonlinear equation forms.

Issue Section:
Research Papers
Keywords:
glulam, composite materials, exp-function method, GRP, natural frequency, beams (structures), dynamic response, dynamics, finite element analysis, glass fibre reinforced composites, nonlinear differential equations, wood
Topics:
Composite materials, Dynamic response, Glued laminated timbers, Wood products, Epoxy adhesives, Glass, Composite building materials, Mathematical physics, Timoshenko beam theory, Instrumentation, Numerical analysis
1.
Mark
,
R.
, 1961, “
Wood-Aluminum Beams Within and Beyond the Elastic Range. Part 1: Rectangular Sections
,”
For. Prod. J.
0015-7473,
11
, pp.
477
–
484
.
2.
Sliker
,
A.
, 1962, “
Reinforced Wood Laminated Beams
,”
For. Prod. J.
0015-7473,
12
, pp.
91
–
96
.
3.
Bohannan
,
B.
, 1962, “
Prestressed Wood Members
,”
For. Prod. J.
0015-7473,
12
, pp.
596
–
602
.
4.
Peterson
,
J.
, 1965, “
Wood Beams Prestressed With Bonded Tension Elements
,”
J. Struct. Eng.
0733-9445,
91
, pp.
103
–
119
.
5.
Lantos
,
G.
, 1970, “
The Flexural Behavior of Steel Reinforced Laminated Timber Beams
,”
Wood Sci.
0043-7700,
2
, pp.
136
–
143
.
6.
Stern
,
E. G.
, and
Kumar
,
V. K.
, 1973, “
Flitch Beams
,”
For. Prod. J.
0015-7473,
23
, pp.
40
–
47
.
7.
Coleman
,
G. E.
, and
Hurst
,
H. T.
, 1974, “
Timber Structures Reinforced With Light Gage Steel
,”
For. Prod. J.
0015-7473,
24
, pp.
45
–
53
.
8.
Hoyle
,
R. J.
, 1975, “
Steel-Reinforced Wood Beam Design
,”
For. Prod. J.
0015-7473,
25
, pp.
17
–
23
.
9.
Bulleit
,
W. M.
, 1984, “
Reinforcement of Wood Materials: A Review
,”
Wood Fiber Sci.
0735-6161,
16
, pp.
391
–
397
.
10.
Plevris
,
N.
, and
Triantafillou
,
T.
, 1992, “
FRP-Reinforcement Wood as Structural Material
,”
J. Mater. Civ. Eng.
0899-1561,
4
, pp.
300
–
317
.
Crossref
Search ADS
 
11.
Plevris
,
N.
, and
Triantafillou
,
T.
, 1995, “
Creep Behavior of FRP-Reinforcement Wood Members
,”
J. Struct. Eng.
0733-9445,
121
, pp.
174
–
186
.
Crossref
Search ADS
 
12.
Davalos
,
J. F.
,
Salim
,
H. A.
, and
Munipalle
,
U.
, 1992, “
Glulam-GRFP Composite Beams for Stress-Laminated T-System Timber Bridges
,”
Proceedings of First International Conference on Advanced Composite Materials in Bridges and Structures CSCE-CGC
, Sherbrooke, QC, Canada, pp.
455
–
463
.
13.
Abdel-Magid
,
B.
,
Dagher
,
H. J.
, and
Kimball
,
T. E.
, 1994, “
The Effect of Composite Reinforcement on Structural Wood
,”
Proceedings of ASCE, Materials Engineering Conference
, San Diego, CA, Nov. 14–16.
14.
Sonti
,
S. S.
,
Davalos
,
J. F.
,
Hernandez
,
R.
,
Moody
,
R. C.
, and
Kim
,
Y.
, 1995, “
Laminated Wood Beams Reinforced With Pultruded Fiber-Reinforced Plastic
,”
Proceedings of the Composites Institute’s 50th Annual Conference and Expo 95
, Cincinnati, OH, pp.
1
–
5
.
15.
Dailey
,
T. H.
, Jr.,
Alison
,
R. A.
,
Minneci
,
J.
, and
Bender
,
R. L.
, 1995, “
Hybrid Composites: Efficient Utilization of Resources by Performance Enhancement of Traditional Engineered Composites With Pultruded Sheets
,”
Proceedings of Composites Institute’s 50th Annual Conference and Expo 95
, Cincinnati, OH, Jan. 30, pp.
1
–
4
.
16.
Dagher
,
H. J.
,
Kimball
,
T. E.
,
Shaler
,
S. M.
, and
Abdel-Magid
,
B.
, 1996, “
Effect of FRP Reinforcement on Low Grade Eastern Hemlock Glulams
,” National Conference on Wood Transportation Structures, Madison, WI, General Technical Report No. FPL-GTR-96.
17.
Kim
,
Y.
,
Davalos
,
J. F.
, and
Barbero
,
E. J.
, 1997, “
Delamination Buckling of FRP Layer in Laminated Wood Beams
,”
Compos. Struct.
0263-8223,
37
, pp.
311
–
320
.
Crossref
Search ADS
 
18.
Romam
,
M.
, and
Blab
,
H. J.
, 2001, “
Design Model for FRP Reinforced Glulam Beams
,”
International Council for Research and Innovation in Building and Construction
, Venice, Italy.
19.
ASTM
, 1998, “
Standard Test Method for Measuring Vibration-Damping Properties of Materials
,” American Society for Testing and Materials, Philadelphia, PA, ASTM Paper No. 756-98, pp.
981
–
992
.
20.
SAE
, 1993, “
Recommended Practice Laboratory Measurement of the Composite Vibration Damping Properties of Materials on a Supporting Steel Bar
,” SAE Paper No. J1637, p.
93
.
21.
Zou
,
G.
,
Naghipour
,
M.
, and
Taheri
,
F.
, 2003, “
A Nondestructive Method for Evaluating Natural Frequency of Glued-Laminated Beams Reinforced With GRP
,”
Nondestr. Test. Eval.
1058-9759,
19
, pp.
53
–
65
.
Crossref
Search ADS
 
22.
Naghipour
,
M.
,
Taheri
,
F.
, and
Zou
,
G.
, 2005, “
Evaluation of Vibration Damping of Glass-Remforced-Polymer-Remforced Glulam Composite Beams
,”
J. Struct. Eng.
0733-9445,
131
, pp.
1044
–
1050
.
Crossref
Search ADS
 
23.
Naghipour
,
M.
,
Mehrzadi
,
M.
,
Taheri
,
F.
, and
Zou
,
G.
, 2009, “
Polynomial Correction Function for Half-Power Bandwidth (HPB) Method of Damping of Glulam Beams Reinforced With E-Glass Reinforced Epoxy Polymer GRP
,”
Can. J. Civ. Eng.
0315-1468,
36
, pp.
241
–
252
.
Crossref
Search ADS
 
24.
Naghipour
,
M.
, and
Mehrzadi
,
M.
, 2007, “
Evaluation of Dynamic Properties of Extra Light Weight Concrete Sandwich Beams Reinforced With CFRP
,”
Steel Compos. Struct.
1229-9367,
7
, pp.
457
–
468
.
Crossref
Search ADS
 
25.
Taheri
,
F.
,
Zou
,
G.
, and
Naghipour
,
M.
, 2005, “
Experimental and Theoretical Investigation Into the Energy Absorption Response of FRP Strengthened Glulam Beams Under Impact Including Damping
,”
For. Prod. J.
0015-7473,
155
, pp.
62
–
70
.
26.
Raftery
,
G. M.
,
Harte
,
A. M.
, and
Rodd
,
P. D.
, 2009, “
Bonding of FRP Materials to Wood Using Thin Epoxy Gluelines
,”
Int. J. Adhes. Adhes.
0143-7496,
29
, pp.
580
–
588
.
Crossref
Search ADS
 
27.
Ribeiro
,
A. S.
,
Jesus
,
A. M. P.
,
Lima
,
A. M.
, and
Lousada
,
J. L. C.
, 2009, “
Study of Strengthening Solutions for Glued-Laminated Wood Beams of Maritime Pine Wood
,”
Constr. Build. Mater.
0950-0618,
23
, pp.
2738
–
2745
.
Crossref
Search ADS
 
28.
He
,
J. H.
, 1999, “
Variational Iteration Method: A Kind of Nonlinear Analytical Technique: Some Examples
,”
Int. J. Non-Linear Mech.
0020-7462,
34
, pp.
699
–
708
.
Crossref
Search ADS
 
29.
He
,
J. H.
, 2003, “
Homotopy Perturbation Method: A New of Nonlinear Analytical Technique
,”
Appl. Math. Comput.
0096-3003,
135
, pp.
73
–
79
.
30.
He
,
J. H.
, 2006, “
Some Asymptotic Methods for Strongly Nonlinear Equations
,”
Int. J. Mod. Phys. B
0217-9792,
20
, pp.
1141
–
99
.
Crossref
Search ADS
 
31.
Abdou
,
M. A.
, and
Soliman
,
A. A.
, 2005, “
New Applications of Variational Iteration Method
,”
Physica D
0167-2789,
211
, pp.
1
–
8
.
Crossref
Search ADS
 
32.
Liang
,
A.
, 2003, “
Asymptotic Wave Solutions for Euler–Bernoulli and Timoshenko Beam by Ray Method and Stationary Phase Method
,” MS thesis,North Carolina State University.
33.
He
,
J. H.
, and
Wu
,
X. H.
, 2006, “
Exp-Function Method for Nonlinear Wave Equation
,”
Chaos, Solitons Fractals
0960-0779,
30
, pp.
700
–
708
.
Crossref
Search ADS
 
34.
Wu
,
X. H.
, and
He
,
J. H.
, 2007, “
Solitary Solutions, Periodic Solutions and Compacton-Like Solutions Using the Exp-Function Method
,”
Comput. Math. Appl.
0898-1221,
54
, pp.
966
–
986
.
Crossref
Search ADS
 
35.
Zhang
,
S.
,
Tong
,
J. L.
, and
Wang
,
W.
, 2009, “
Exp-Function Method for a Nonlinear Ordinary Differential Equation and New Exact Solutions of the Dispersive Long Wave Equations
,”
Comput. Math. Appl.
0898-1221,
58
, pp.
2294
–
2299
.
Crossref
Search ADS
 
36.
Dai
,
C. Q.
,
Cen
,
X.
, and
Wu
,
S. S.
, 2009, “
Exact Travelling Wave Solutions of the Discrete Sine-Gordon Equation Obtained via the Exp-Function Method
,”
Nonlinear Anal.
,
70
, pp.
58
–
63
.
Crossref
Search ADS
 
37.
Khani
,
F.
,
Hamedi–Nezhad
,
S.
,
Darvishi
,
M. T.
, and
Ryu
,
S. W.
, 2009, “
New Solitary Wave and Periodic Solutions of the Foam Drainage Equation Using the Exp-Function Method
,”
Nonlinear Anal.: Real World Appl.
1468-1218,
10
, pp.
1904
–
1911
.
Crossref
Search ADS
 
38.
Fu
,
H. M.
, and
Dai
,
Z. D.
, 2009, “
Double Exp-Function Method and Application
,”
Int. J. Nonlinear Sci. Numer. Simul.
1565-1339,
10
, pp.
927
–
933
.
39.
Dai
,
Z. D.
,
Wang
,
C. J.
,
Lin
,
S. Q.
,
Li
,
D. L.
, and
Mu
,
G.
, 2010, “
The Three-Wave Method for Nonlinear Evolution Equations
,”
Nonl. Sci. Lett. A
,
1
, pp.
77
–
82
.
40.
He
,
J. H.
, 2008, “
An Elementary Introduction to Recently Developed Asymptotic Methods and Nanomechanics in Textile Engineering
,”
Int. J. Mod. Phys. B
0217-9792,
22
, pp.
3487
–
3578
.
Crossref
Search ADS
 
41.
ASTM
, 2001, “
Methods of Static Tests of Timber in Structural Sizes
,” American Society for Testing and Materials, Philadelphia, PA, ASTM Paper No. D198-99.
42.
Borden Chemical, Inc.
, 1994, Adhesive and Resins, TDS Paper No. LT-5210IB Technical Data Sheet.
43.
ASTM
, 2000, “
Standard Specification for Adhesives for Structural Laminated Wood Products for Use Under Exterior (Wet Use) Exposure Conditions
,” American Society for Testing and Materials, Philadelphia, PA, ASTM Paper No. D2559, pp.
981
–
992
.
44.
Mallick
,
P. K.
, 1988,
Fiber-Reinforced Composites: Materials, Manufacturing and Design
,
Marcel Dekker
,
New York
.
45.
Naghipour
,
M.
,
Daniali
,
H. M.
, and
Hashemi Kachapi
,
S. H. A.
, 2008, “
Numerical Simulation of Composite Plates to be Used for Optimization of Mobile Bridge Deck
,”
World Applied Science Journal
1818-4952,
4
, pp.
681
–
690
.
Copyright © 2011
 by American Society of Mechanical Engineers
You do not currently have access to this content.