Abstract
Elastic coupling is extensively used for passive control of modern structures. This design philosophy has been extensively explored in composite beams, which are inherently inhomogeneous and anisotropic. Such in-depth investigation is not available for homogeneous-anisotropic beams. This paper investigates elastic coupling in homogeneous-anisotropic beam with elliptical cross section using variational asymptotic method (VAM). It is observed that the mere introduction of anisotropy does not couple the system completely. The coupling is tuneable and tailorable, depending on the material properties, their spatial distribution (homogeneity/inhomogeneity), and the geometrical parameters of the beam.
Issue Section:
Technical Brief
Topics:
Anisotropy
References
1.
Bagherpour
, T.
, Li
, X.
, Manolas
, D.
, and Riziotis
, V.
, 2018
, “Modeling of Material Bend-Twist Coupling on Wind Turbine Blades
,” Compos. Struct.
, 193
, pp. 237
–246
. 2.
de Goeij
, W.
, van Tooren
, M.
, and Beukers
, A.
, 1999
, “Implementation of Bending-Torsion Coupling in the Design of a Wind-Turbine Rotor-Blade
,” Appl. Energy
, 63
(3
), pp. 191
–207
. 3.
Hayat
, K.
, and Ha
, S. K.
, 2015
, “Load Mitigation of Wind Turbine Blade by Aeroelastic Tailoring Via Unbalanced Laminates Composites
,” Compos. Struct.
, 128
, pp. 122
–133
. 4.
Shams
, S.
, Sadr
, M. H.
, and Badiei
, D.
, 2021
, “Nonlinear Aeroelasticity of High-Aspect-Ratio Wings With Laminated Composite Spar
,” J. Braz. Soc. Mech. Sci. Eng.
, 43
(7
), p. 334
. 5.
Mansfield
, E. H.
, and Sobey
, A. J.
, 1979
, “The Fibre Composite Helicopter Blade: Part I: Stiffness Properties: Part Ii: Prospects for Aeroelastic Tailoring
,” Aeronaut. Q.
, 30
(2
), pp. 413
–449
. 6.
Hong
, C.
, and Chopra
, I.
, 1986
, “Aeroelastic Stability Analysis of a Composite Bearingless Rotor Blade
,” J. Am. Helicopter Soc.
, 31
(4
), pp. 29
–35
. 7.
Hong
, C.
, and Chopra
, I.
, 1985
, “Aeroelastic Stability Analysis of a Composite Rotor Blade
,” J. Am. Helicopter Soc.
, 30
(2
), pp. 57
–67
. 8.
Hashin
, Z.
, 1967
, “Plane Anisotropic Beams
,” ASME J. Appl. Mech.
, 34
(2
), pp. 257
–262
. 9.
Karttunen
, A. T.
, and von Hertzen
, R.
, 2016
, “On the Foundations of Anisotropic Interior Beam Theories
,” Compos. Part B: Eng.
, 87
, pp. 299
–310
. 10.
Kosmatka
, J. B.
, and Dong
, S. B.
, 1991
, “Saint-Venant Solutions for Prismatic Anisotropic Beams
,” Int. J. Solids. Struct.
, 28
(7
), pp. 917
–938
. 11.
Ie
, C.
, and Kosmatka
, J.
, 1993
, “Saint-Venant Elasticity Solutions of a Tip-Loaded Anisotropic Cantilevered Beam With An Elliptical Section
,” Compos. Eng.
, 3
(12
), pp. 1149
–1164
. 12.
Omri Rand
, V. R.
, 2005
, Analytical Methods in Anisotropic Elasticity: With Symbolic Computational Tools
, 1st ed., Birkhäuser
, Boston, MA
.13.
Berdichevskii
, V. L.
, 1979
, “Variational-Asymptotic Method of Constructing a Theory of Shells. PMM Vol. 43, No.4, 1979, Pp. 664–687
,” J. Appl. Math. Mech.
, 43
(4
), pp. 711
–736
. 14.
Berdichevskii
, V. L.
, and Khan’ Chau
, L.
, 1980
, “High-Frequency Long-Wave Shell Vibration
,” J. Appl. Math. Mech.
, 44
(4
), pp. 520
–525
. 15.
Berdichevskii
, V.
, 1981
, “On the Energy of an Elastic Rod
,” J. Appl. Math. Mech.
, 45
(4
), pp. 518
–529
. 16.
Berdichevskii
, 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
. 17.
Berdichevsky
, V.
, Armanios
, E.
, and Badir
, A.
, 1992
, “Theory of Anisotropic Thin-Walled Closed-Cross-Section Beams
,” Compos. Eng.
, 2
(5–7
), pp. 411
–432
. 18.
Murakami
, H.
, Reissner
, E.
, and Yamakawa
, J.
, 1996
, “Anisotropic Beam Theories With Shear Deformation
,” ASME J. Appl. Mech.
, 63
(3
), pp. 660
–668
. 19.
Reissner
, E.
, 1984
, “On a Certain Mixed Variational Theorem and a Proposed Application
,” Int. J. Numer. Methods Eng.
, 20
(7
), pp. 1366
–1368
. 20.
Bauchau
, O. A.
, 1985
, “A Beam Theory for Anisotropic Materials
,” ASME J. Appl. Mech.
, 52
(2
), pp. 416
–422
. 21.
Parker
, D.
, 1979
, “An Asymptotic Analysis of Large Deflections and Rotations of Elastic Rods
,” Int. J. Solids. Struct.
, 15
(5
), pp. 361
–377
. 22.
Danielson
, D. A.
, and Hodges
, D. H.
, 1987
, “Nonlinear Beam Kinematics by Decomposition of the Rotation Tensor
,” ASME J. Appl. Mech.
, 54
(2
), pp. 258
–262
. 23.
Danielson
, D. A.
, and Hodges
, D. H.
, 1988
, “A Beam Theory for Large Global Rotation, Moderate Local Rotation, and Small Strain
,” ASME J. Appl. Mech.
, 55
(1
), pp. 179
–184
. 24.
Yu
, W.
, and Hodges
, D. H.
, 2004
, “Elasticity Solutions Versus Asymptotic Sectional Analysis of Homogeneous, Isotropic, Prismatic Beams
,” ASME J. Appl. Mech.
, 71
(1
), pp. 15
–23
. 25.
Hodges
, D. H.
, 2006
, Nonlinear Composite Beam Theory.
Progress in Astronautics and Aeronautics, Vol. 213
. American Institute of Aeronautics and Astronautics
.Copyright © 2023 by ASME
You do not currently have access to this content.
