This paper deals with the dynamic analysis of reinforced thin-walled structures by means of refined one-dimensional models. Complex reinforced structures are considered which are built by using different components: skin, ribs, and stringers. Higher-order one-dimensional model based on the Carrera unified formulation (CUF) are used to model panels, stringer, and ribs by referring to a unique model. The finite element method (FEM) is used to provide a solution that deals with any boundary condition configuration. The structure is geometrically linear and the materials are isotropic and elastic. The dynamic behavior of a number of reinforced thin-walled cylindrical structures have been analyzed. The effects of the reinforcements (ribs and stringers) are investigated in terms of natural frequencies and modal-shapes. The results show a good agreement with those from commercial codes by reducing the computational costs in terms of degrees of freedom (DOFs).

References

References
1.
Argyris
,
J. M.
, and
Kelsey
,
S.
,
1960
,
Energy Theorems and Structural Analysis
,
Butterworths
,
London
.
2.
Bruhn
,
E. F.
,
1973
,
Analysis and Design of Flight Vehicle Structures
,
Tri-State Offset Company
, Cincinnati, OH.
3.
Vecchio
,
F. J.
, and
Collins
,
M. P.
,
1986
, “
The Modified Compression-Field Theory for Reinforced Concrete Elements Subjected to Shear
,”
ACI J.
,
83
(
2
), pp.
219
231
.
4.
Schade
,
H.A.
,
1940
, “
The Orthogonally Stiffened Plate Under Uniform Lateral Load
,”
ASME J. Appl. Mech.
,
62
, pp.
143
146
.
5.
Kendrick
,
S.
,
1956
, “
The Analysis of a Flat Plated Grillage
,”
Eur. Shipbuilding
,
5
, pp.
4
10
.
6.
Lin
,
Y. K.
,
1960
, “
Free Vibration of Continuous Skin-Stringer Panels
,”
J. Appl. Mech.
,
27
, pp.
669
676
.10.1115/1.3644080
7.
Xu
,
H.
,
Du
,
J.
, and
Li
,
W. L.
,
2010
, “
Vibrations of Rectangular Plates Reinforced by Any Number of Beams of Arbitrary Lengths and Placement Angles
,”
J. Sound Vibration
,
329
, pp.
3759
3779
.10.1016/j.jsv.2010.03.023
8.
Turvey
,
G.
,
1971
, “
A Contribution to the Elastic Stability of Thin Walled Structures Fabricated From Isotropic and Orthotropic Materials
,” Ph.D. dissertation, Univerity of Birmingham, Birmingham, AL.
9.
Cheung
,
Y. K.
, and
Delcourt
,
C.
,
1977
, “
Buckling and Vibration of Thin Flat-Walled Structures Continuous Over Several Spans
,
Proc. Inst. Civil Eng., Part II
,
63
(
2
), pp.
93
103
.10.1680/iicep.1977.3295
10.
Liew
,
K. M.
,
Xiang
,
Y.
,
Kitipornchai
,
S.
, and
Meek
,
J. L.
,
1995
, “
Formulation of Mindlin-Engesser Model for Stiffened Plate Vibration
,”
Comput. Methods Appl. Mech. Eng.
,
120
, pp.
339
353
.10.1016/0045-7825(94)00064-T
11.
Dozio
,
L.
, and
Ricciardi
,
M.
,
2009
, “
Free Vibration Analysis of Ribbed Plates by a Combined Analytical-Numerical Method
,”
J. Sound Vibration
,
319
, pp.
681
697
.10.1016/j.jsv.2008.06.024
12.
Bhimaraddi
,
A.
,
Carr
,
A. J.
, and
Moss
,
P. J.
,
1989
, “
Finite Element Analysis of Laminated Shells of Revolution With Laminated Stiffeners
,
Comput. Struct.
,
33
, pp.
295
305
.10.1016/0045-7949(89)90153-3
13.
Venkatesh
,
A.
, and
Rao
,
K. P.
,
1985
, “
Analysis of Laminated Shells of Revolution With Laminated Stiffeners Using a Doubly Curved Quadrilateral Finite Element
,”
Comput. Struct.
,
20
, pp.
669
682
.10.1016/0045-7949(85)90028-8
14.
Bouabdallah
,
M. S.
, and
Batoz
,
J. L.
,
1996
, “
Formulation and Evaluation of a Finite Element Model for the Linear Analysis of Stiffened Composite Cylindrical Panels
,”
Finite Elements in Analysis and Design
,
21
, pp.
669
682
.10.1016/0168-874X(95)00047-W
15.
Mustafa
,
B. A. J.
, and
Ali
,
R.
,
1987
, “
Prediction of Natural Frequency of Vibration of Stiffened Cylindrical Shells and Orthogonally Stiffened Curved Panels
,”
J. Sound Vibration
,
43
, pp.
317
327
.10.1016/S0022-460X(87)80218-3
16.
Amabili
,
M.
,
2008
,
Nonlinear Vibrations and Stability of Shells and Plates
,
Cambridge University Press
,
New York
.
17.
Euler
,
L.
,
1744
,
Theory of Elasticity
,
Bousquet
,
Lausanne/Geneva
, Switzerland.
18.
Timoshenko
,
S. P.
, and
Goodier
,
J. N.
,
1970
,
Theory of Elasticity
,
McGraw-Hill
,
New York
.
19.
Timoshenko
,
S. P.
,
1921
, “
On the Correction for Shear of the Differential Equation for Transverse Vibration of Prismatic Bars
,”
Philos. Mag.
,
41
, pp.
744
746
.10.1080/14786442108636264
20.
Stephen
,
N. G.
,
1980
, “
Timoshenko's Shear Coefficient From a Beam Subjected to Gravity Loading
,
ASME J. Appl. Mech.
,
47
, pp.
121
127
.10.1115/1.3153589
21.
Hutchinson
,
J. R.
,
2001
, “
Shear Coefficients for Timoshenko Beam Theory
,
ASME J. Appl. Mech.
,
68
, pp.
87
92
.10.1115/1.1349417
22.
Jensen
,
J. J.
,
1983
, “
On the Shear Coefficients in Thimoshenko's Beam Theory
,”
J. Sound Vibration
,
87
, pp.
621
635
.10.1016/0022-460X(83)90511-4
23.
Schardt
,
R.
,
1966
, “
Eine Erweiterung Der Technischen Biegetheorie Zur Berechnung Prismatischer Faltwerke
,”
Der Stahlbau
,
35
, pp.
161
171
.
24.
Schardt
,
R.
,
1994
, “
Generalized Beam Theory—An Adequate Method for Coupled Stability Problems
,”
Thin-Walled Structures
,
19
, pp.
161
180
.10.1016/0263-8231(94)90027-2
25.
Schardt
,
R.
, and
Heinz
,
D.
,
1991
, “
Vibrations of Thin-Walled Prismatic Structures Under Simultaneous Static Load Using Generalized Beam Theory
,”
Structural Dynamics
,
O. T. Bruhns, H. L. Jessberger, A. N. Kounadis, W. B. Kraetzig, K. Meskouris, H.-J. Niemann, G. Schmidt, G. I. Schueller, and F. Stangenberger, eds., A A Balkema Publishers, Rotterdam, The Netherlands,
pp.
961
927
.
26.
Bebiano
,
R.
,
Silvestre
,
N.
, and
Camotim
,
D.
,
2008
, “
Local and Global Vibration of Thin-Walled Members Subjected to Compression and Non-Uniform Bending
,”
J. Sound Vibration
,
315
, pp.
509
535
.10.1016/j.jsv.2008.02.036
27.
Berdichevsky
,
V. L.
, and
Starosel'skii
,
L. A.
,
1983
, “
On the Theory of Curvilinear Timoshenko-Type Rods
,
J. Appl. Math. Mech.
,
47
(
6
), pp.
809
817
.10.1016/0021-8928(83)90121-1
28.
Volovoi
,
V. V.
, and
Hodges
,
D. H.
,
2000
, “
Theory of Anisotropic Thin-Walled Beams
,”
ASME J. Appl. Mech.
,
67
, pp.
453
459
.10.1115/1.1312806
29.
Yu
,
W.
,
Volovoi
,
V. V.
,
Hodges
,
D. H.
, and
Hong
,
X.
,
2002
, “
Validation of the Variational Asymptotic Beam Sectional Analysis (VABS)
,
AIAA J.
,
40
, pp.
2105
2113
.10.2514/2.1545
30.
El Fatmi
,
R.
,
2007
, “
Non-Uniform Warping Including the Effects of Torsion and Shear Forces. Part I. A General Beam Theory
,”
Int. J. Solids Struct.
,
44
(
18-19
), pp.
5912
5929
.10.1016/j.ijsolstr.2007.02.006
31.
El Fatmi
,
R.
,
2007
, “
Non-Uniform Warping Including the Effects of Torsion and Shear Forces. Part II. Analytical and Numerical Applications
,”
Int. J. Solids Struct.
,
44
(
18-19
), pp.
5930
5952
.10.1016/j.ijsolstr.2007.02.005
32.
Wittrick
,
W. H.
, and
Williams
,
F. W.
,
1971
, “
A General Algorithm for Computing Natural Frequencies of Elastic Structures
,
Q. J. Mech. Appl. Math.
,
24
, pp.
263
284
.10.1093/qjmam/24.3.263
33.
Carrera
,
E.
,
2002
, “
Theories and Finite Elements for Multilayered, Anisotropic, Composite Plates and Shells
,”
Arch. Comput. Methods Eng.
,
9
(
2
), pp.
87
140
.10.1007/BF02736649
34.
Carrera
,
E.
,
2003
, “
Theories and Finite Elements for Multilayered Plates and Shells: A Unified Compact Formulation With Numerical Assessment and Benchmarking
,”
Arch. Comput. Methods Eng.
,
10
(
3
), pp.
216
296
.10.1007/BF02736224
35.
Carrera
,
E.
, and
Brischetto
,
S.
,
2008
, “
Analysis of Thickness Locking In Classical, Refined And Mixed Multilayered Plate Theories
,”
Compos. Struct.
,
82
(
4
), pp.
549
562
.10.1016/j.compstruct.2007.02.002
36.
Carrera
,
E.
,
Brischetto
,
S.
, and
Robaldo
,
A.
,
2008
, “
Variable Kinematic Model For The Analysis Of Functionally Graded Material Plates
,”
AIAA J.
,
46
, pp.
194
203
.10.2514/1.32490
37.
Carrera
,
E.
,
Giunta
,
G.
,
Nali
,
P.
, and
Petrolo
,
M.
,
2010
, “
Refined Beam Elements With Arbitrary Cross-Section Geometries
,”
Comput. Struct.
,
88
(
5-6
), pp.
283
293
.10.1016/j.compstruc.2009.11.002
38.
Carrera
,
E.
,
Petrolo
,
M.
, and
Zappino
,
E.
,
2012
, “
Performance of CUFApproach to Analyze the Structural Behavior Of Slender Bodies
.”
J. Struct. Eng.
,
138
(
2
), pp.
285
297
.10.1061/(ASCE)ST.1943-541X.0000402
39.
Carrera
,
E.
,
Petrolo
,
M.
, and
Nali
,
P.
2010
, “
Unified Formulation Applied To Free Vibrations Finite Element Analysis of Beams With Arbitrary Section
,”
Shock and Vibrations
,
17
, pp.
1
18
.10.3233/SAV-2010-0528
40.
Carrera
,
E.
,
Petrolo
,
M.
, and
Varello
,
A.
,
2012
, “
Advanced Beam Formulations for Free Vibration Analysis of Conventional and Joined Wings
,”
J. Aerospace Engin.
,
25
(
2
), pp.
282
293
.10.1061/(ASCE)AS.1943-5525.0000130
41.
Carrera
,
E.
,
Zappino
,
E.
, and
Petrolo
,
M.
,
2012
, “
Analysis of Thin-Walled Structures With Longitudinal And Transversal Stiffeners
,”
ASME J. Appl. Mech.
(in press).10.1115/1.4006939
42.
Washizu
,
K.
,
1975
,
Variational Methods in Elasticity and Plasticity
,
Pergamon
,
Oxford
.
43.
Carrera
,
E.
, and
Giunta
,
G.
,
2010
, “
Refined Beam Theories Based On A Unified Formulation
,”
Int. J. Appl. Mech.
,
2
(
1
), pp.
117
143
.10.1142/S1758825110000500
44.
Carrera
,
E.
,
Petrolo
,
M.
, and
Nali
,
P.
,
2011
, “
Unified Formulation Applied To Free Vibrations Finite Element Analysis Of Beams With Arbitrary Section
,”
Shock and Vibrations
,
18
(
3
), pp.
485
502
.10.3233/SAV-2010-0528
45.
Carrera
,
E.
, and
Petrolo
,
M.
,
2011
, “
On the Effectiveness of Higher-Order Terms In Refined Beam Theories
,”
J. Appl. Mech.
,
78
(
3
).10.1115/1.4002207
46.
Carrera
,
E.
, and
Giunta
,
G.
,
2010
, “
Refined Beam Theories Based on a Unified Formulation
,”
Int. J. Appl. Mech.
,
2
, pp.
117
143
.10.1142/S1758825110000500
47.
Bathe
,
K. J.
,
1996
,
Finite Element Procedure
,
Prentice-Hall
,
NY
.
48.
Tsai
,
S. W.
,
1988
,
Composites Design, 4th ed.
,
Think Composites
,
Dayton
.
49.
Reddy
,
J. N.
,
2004
,
Mechanics of Laminated Composite Plates and Shells. Theory and Analysis
,
2nd ed.
,
CRC Press
,
Boca Raton
.
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