Nonlinear dynamics and mode aberration of rotating plates and shells are discussed in this work. The mathematical formalism is based on the one-dimensional (1D) Carrera unified formulation (CUF), which enables to express the governing equations and related finite element arrays as independent of the theory approximation order. As a consequence, three-dimensional (3D) solutions accounting for couplings due to geometry, material, and inertia can be included with ease and with low computational costs. Geometric nonlinearities are incorporated in a total Lagrangian scenario and the full Green-Lagrange strains are employed to outline accurately the equilibrium path of structures subjected to inertia, centrifugal forces, and Coriolis effect. A number of representative numerical examples are discussed, including multisection blades and shells with different radii of curvature. Particular attention is focused on the capabilities of the present formulation to deal with nonlinear effects, and comparison with s simpler linearized approach shows evident differences, particularly in the case of deep shells.
Issue Section:
Research Papers
References
1.
Rao
, J.
, 1973
, “Natural Frequencies of Turbine Blading—A Survey
,” Shock Vib. Dig.
, 5
(10
), pp. 3
–16
.2.
Carniege
, W.
, 1964
, “Vibration of Pre-twisted Cantilever Blading Allowing for Rotary Inertia and Shear Deflection
,” Int. J. Eng. Sci.
, 6
(2
), pp. 105
–109
.3.
Putter
, S.
, and Manor
, H.
, 1978
, “Natural Frequencies of Radial Rotating Beams
,” J. Sound Vib.
, 56
(2
), pp. 175
–185
.4.
Ansari
, K. A.
, 1986
, “On the Importance of Shear Deformation, Rotatory Inertia, and Coriolis Forces in Turbine Blade Vibrations
,” ASME J. Eng. Gas Turbines Power
, 108
(2
), pp. 319
–324
.5.
Chandra
, R.
, and Chopra
, I.
, 1992
, “Experimental-Theoretical Investigation of the Vibration Characteristics of Rotating Composite Box Beams
,” J. Aircr.
, 29
(4
), pp. 657
–664
.6.
Jung
, S. N.
, Nagaraj
, V. T.
, and Chopra
, I.
, 2001
, “Refined Structural Dynamics Model for Composite Rotor Blades
,” AIAA J.
, 39
(2
), pp. 339
–348
.7.
Hodges
, D. H.
, 2006
, Nonlinear Composite Beam Theory
, American Institute of Aeronautics and Astronautics
, Reston, VA
.8.
Cesnik
, C. E. S.
, and Hodges
, D. H.
, 1997
, “Vabs: A New Concept for Composite Rotor Blade Cross-Sectional Modeling
,” J. Am. Helicopter Soc.
, 42
(1
), pp. 27
–38
.9.
Leissa
, A. W.
, 1980
, “Vibrations of Turbine Engine Blades by Shell Analysis
,” Shock Vib. Dig.
, 12
(11
), pp. 3
–10
.10.
Leissa
, A. W.
, Lee
, J. K.
, and Wang
, A. J.
, 1982
, “Rotating Blade Vibration Analysis Using Shells
,” ASME J. Eng. Power
, 104
(2
), pp. 296
–302
.11.
Hu
, X. X.
, Sakiyama
, T.
, Matsuda
, H.
, and Morita
, C.
, 2004
, “Fundamental Vibration of Rotating Cantilever Blades With Pre-Twist
,” J. Sound Vib.
, 271
(1–2
), pp. 47
–66
.12.
Kee
, Y.-J.
, and Kim
, J.-H.
, 2004
, “Vibration Characteristics of Initially Twisted Rotating Shell Type Composite Blades
,” Compos. Struct.
, 64
(2
), pp. 151
–159
.13.
Kang
, H.
, Chang
, C.
, Saberi
, H.
, and Ormiston
, R.
, 2014
, “Assessment of Beam and Shell Elements for Modeling Rotorcraft Blades
,” J. Aircr.
, 51
(2
), pp. 520
–531
.14.
Sze
, K. Y.
, Liu
, X. H.
, and Lo
, S. H.
, 2004
, “Popular Benchmark Problems for Geometric Nonlinear Analysis of Shells
,” Finite Elem. Anal. Des.
, 40
(11
), pp. 1551
–1569
.15.
Kee
, Y.-J.
, and Shin
, S.-J.
, 2015
, “Structural Dynamic Modeling for Rotating Blades Using Three Dimensional Finite Elements
,” J. Mech. Sci. Technol.
, 29
(4
), pp. 1607
–1618
.16.
Bauchau
, O. A.
, Bottasso
, C. L.
, and Nikishkov
, Y. G.
, 2001
, “Modeling Rotorcraft Dynamics With Finite Element Multibody Procedures
,” Math. Comput. Model.
, 33
(10–11
), pp. 1113
–1137
.17.
Bauchau
, O. A.
, and Chiang
, W.
, 1994
, “Dynamic Analysis of Bearingless Tail Rotor Blades Based on Nonlinear Shell Models
,” J. Aircr.
, 31
(6
), pp. 1402
–1410
.18.
Bauchau
, O. A.
, Choi
, J.-Y.
, and Bottasso
, C. L.
, 2002
, “On the Modeling of Shells in Multibody Dynamics
,” Multibody Syst. Dyn.
, 8
(4
), pp. 459
–489
.19.
Yu
, W.
, Hodges
, D. H.
, and Volovoi
, V. V.
, 2002
, “Asymptotic Generalization of Reissner Mindlin Theory: Accurate Three-Dimensional Recovery for Composite Shells
,” Comput. Methods Appl. Mech. Eng.
, 191
(44
), pp. 5087
–5109
.20.
Hodges
, D. H.
, Atilgan
, A. R.
, and Danielson
, D. A.
, 1993
, “A Geometrically Nonlinear Theory of Elastic Plates
,” ASME J. Appl. Mech.
, 60
(1
), pp. 109
–116
.21.
Hodges
, D. H.
, Yu
, W.
, and Patil
, M. J.
, 2009
, “Geometrically-Exact, Intrinsic Theory for Dynamics of Moving Composite Plates
,” Int. J. Solids Struct.
, 46
(10
), pp. 2036
–2042
.22.
Carrera
, E.
, Filippi
, M.
, and Zappino
, E.
, 2013
, “Laminated Beam Analysis by Polynomial, Trigonometric, Exponential and Zig-Zag Theories
,” Eur. J. Mech. A/Solids
, 41
, pp. 58
–69
.23.
Pagani
, A.
, de Miguel
, A.
, Petrolo
, M.
, and Carrera
, E.
, 2016
, “Analysis of Laminated Beams Via Unified Formulation and Legendre Polynomial Expansions
,” Compos. Struct.
, 156
, pp. 78
–92
.24.
Kaleel
, I.
, Petrolo
, M.
, Carrera
, E.
, and Waas
, A. M.
, 2017
, “Micromechanical Progressive Failure Analysis of Fiber-Reinforced Composite Using Refined Beam Models
,” ASME J. Appl. Mech.
, 85
(2
), p. 021004
.25.
Carrera
, E.
, Pagani
, A.
, and Petrolo
, M.
, 2013
, “Classical, Refined and Component-Wise Theories for Static Analysis of Reinforced-Shell Wing Structures
,” AIAA J.
, 51
(5
), pp. 1255
–1268
.26.
Carrera
, E.
, and Pagani
, A.
, 2016
, “Accurate Response of Wing Structures to Free Vibration, Load Factors and Non-Structural Masses
,” AIAA J.
, 54
(1
), pp. 227
–241
.27.
Filippi
, M.
, and Carrera
, E.
, 2016
, “Capabilities of 1D CUF-Based Models to Analyse Metallic/Composite Rotors
,” Adv. Aircr. Spacecr. Sci.
, 3
(1
), pp. 1
–14
.28.
Carrera
, E.
, and Filippi
, M.
, 2016
, “A Refined One-Dimensional Rotordynamics Model With Three-Dimensional Capabilities
,” J. Sound Vib.
, 366
, pp. 343
–356
.29.
Pagani
, A.
, and Carrera
, E.
, 2018
, “Unified Formulation of Geometrically Nonlinear Refined Beam Theories
,” Mech. Adv. Mater. Struct.
, 25
(1
), pp. 15
–31
.30.
Pagani
, A.
, and Carrera
, E.
, 2017
, “Large-Deflection and Post-Buckling Analyses of Laminated Composite Beams by Carrera Unified Formulation
,” Compos. Struct.
, 170
, pp. 40
–52
.31.
Carrera
, E.
, Cinefra
, M.
, Petrolo
, M.
, and Zappino
, E.
, 2014
, Finite Element Analysis of Structures Through Unified Formulation
, Wiley
, Chichester, UK
.32.
Carrera
, E.
, Filippi
, M.
, and Zappino
, F.
, 2013
, “Free Vibration Analysis of Rotating Composite Blades Via Carrera Unified Formulation
,” Compos. Struct.
, 106
, pp. 317
–325
.33.
Carrera
, E.
, and Filippi
, M.
, 2014
, “Variable Kinematic One-Dimensional Finite Elements for the Analysis of Rotors Made of Composite Materials
,” ASME J. Eng. Gas Turbines Power
, 136
(9
), p. 092501
.34.
Entezari
, A.
, Filippi
, M.
, and Carrera
, E.
, 2017
, “On Dynamic Analysis of Variable Thickness Disks and Complex Rotors Subjected to Thermal and Mechanical Prestresses
,” J. Sound Vib.
, 405
, pp. 68
–85
.
You do not currently have access to this content.
