Research Papers: Gas Turbines: Structures and Dynamics

Variable Kinematic One-Dimensional Finite Elements for the Analysis of Rotors Made of Composite Materials

[+] Author and Article Information
E. Carrera

Department of Mechanical
and Aerospace Engineering,
Politecnico di Torino,
Corso Duca degli Abruzzi 24,
Torino 10129, Italy;
School of Aerospace, Mechanical
and Manufacturing Engineering,
RMIT University,
Melbourne, Australia
e-mail: erasmo.carrera@polito.it

M. Filippi

Department of Mechanical
and Aerospace Engineering,
Politecnico di Torino,
Corso Duca degli Abruzzi 24,
Torino 10129, Italy
e-mail: matteo.filippi@polito.it

Contributed by the Structures and Dynamics Committee of ASME for publication in the JOURNAL OF ENGINEERING FOR GAS TURBINES AND POWER. Manuscript received February 18, 2014; final manuscript received February 24, 2014; published online April 18, 2014. Editor: David Wisler.

J. Eng. Gas Turbines Power 136(9), 092501 (Apr 18, 2014) (11 pages) Paper No: GTP-14-1109; doi: 10.1115/1.4027192 History: Received February 18, 2014; Revised February 24, 2014

This paper deals with the dynamic response of rotors made of anisotropic, laminated composite materials. It is a sequel to the authors’ previous work, which was devoted to the rotordynamics of metallic structures. The used variable kinematic one-dimensional models describe any cross-sectional deformation of the rotor and go beyond the plane strain assumptions of classical Euler–Bernoulli and Timoskenko beam theories. Refined theories are obtained by applying the Carrera unified formulation, which is extended here to the rotordynamics of multilayered composites. The displacement variables over the rotor cross section x-z plane are approximated by x,z polynomials of any order N. Thin-walled cylindrical shafts and boxes are analyzed. These structures are made of unidirectional layers, whose fiber orientation can vary with respect to the rotor–axis as well as in the x-z plane. Several analyses have been carried out to determine the vibrational response as a function of the rotating speed. Classical beam theories are obtained as particular cases and results available in the literature, including shell results, are used to assess the presented theory. The proposed refined models are very effective in investigating the dynamic behavior of laminated composite rotors.

Copyright © 2014 by ASME
Your Session has timed out. Please sign back in to continue.


Zinberg, H., and Symmonds, M. F., 1970, “The Development of an Advanced Composite Tail Rotor Driveshaft,” 26th Annual National Forum of the American Helicopter Society, Washington, DC, June 16–18.
Zorzi, E., and Giordano, J. C., 1985, “Composite Shaft Rotor Dynamic Evaluation,” ASME Design Engineering Conference on Mechanical Vibrations and Noise, Cincinnati, OH, September 10–13, ASME Paper No. 85-DET-114.
Bauchau, O. A., 1981, “Design, Manufacturing and Testing of High Speed Rotating Graphite/Epoxy Shafts,” Ph.D. thesis, Department of Aeronautics and Astronautics, MIT, Cambridge, MA.
Bauchau, O. A., 1983, “Optimal Design of High Speed Rotating Graphite/Epoxy Shafts,” J. Compos. Mater., 17(2), pp. 170–181. [CrossRef]
Bert, C. W., and Kim, C. D., 1992, “The Effect of Bending–Twisting Coupling on the Critical Speed of a Drive Shaft,” 6th Japan–U.S. Conference on Composite Materials, Orlando, FL, June 22–24.
Bert, C. W., and Kim, C. D., 1995, “Whirling of Composite-Material Driveshafts Including Bending–Twisting Coupling and Transverse Shear Deformation,” ASME J. Vib. Acoust., 17, pp. 17–21. [CrossRef]
Chen, L. W., and Peng, W. K., 1998, “The Stability Behavior of Rotating Composite Shafts Under Axial Compressive Loads,” Compos. Struct., 41(3–4), pp. 253–263. [CrossRef]
Chang, M. Y., Chen, J. K., and Chang, C. Y., 2004, “A Simple Spinning Laminated Composite Shaft Model,” Int. J. Solids Struct., 41(3–4), pp. 637–662. [CrossRef]
Singh, S. P., and Gupta, K., 1996, “Compostite Shaft Rotordynamic Analysis Using a Layerwise Theory,” J. Sound Vib., 191(5), pp. 739–756. [CrossRef]
Gubran, H. B. H., and Gupta, K., 2005, “The Effect of Stacking Sequence and Coupling Mechanisms on the Natural Frequencies of Composite Shafts,” J. Sound Vib., 282(1–2), pp. 231–248. [CrossRef]
Sino, R., Baranger, T. N., Chatelet, E., and Jacquet, G., 2008, “Dynamic Analysis of a Rotating Composite Shaft,” Compos. Sci. Technol., 68(2), pp. 337–345. [CrossRef]
Song, O., and Librescu, L., 1997, “Anisotropy and Structural Coupling on Vibration and Instability of Spinning Thin-Walled Beams,” J. Sound Vib., 204(3), pp. 477–494. [CrossRef]
Song, O., Librescu, L., and Jeong, N.-H., 2000, “Vibration and Stability of Pretwisted Spinning Thin-Walled Composite Beams Featuring Bending–Bending Elastic Coupling,” J. Sound Vib., 237(3), pp. 513–533. [CrossRef]
Na, S., Yoon, H., and Librescu, L., 2006, “Effect of Taper Ratio on Vibration and Stability of a Composite Thin-Walled Spinning Shaft,” Thin-Walled Struct., 44(3), pp. 362–371. [CrossRef]
Kim, C. D., and Bert, C. W., 1993, “Critical Speed Analysis of Laminated Composite, Hollow Drive Shafts,” Compos. Eng., 3(7–8), pp. 633–644. [CrossRef]
Ramezani, S., and Ahmadian, M. T., 2009, “Free Vibration Analysis of Rotating Laminated Cylindrical Shells Under Different Boundary Conditions Using a Combination of the Layerwise Theory and Wave Propagation Approach,” Trans. B: Mech. Eng., 16, pp. 168–176.
Zhao, X., Liew, K. M., and Ng, T. Y., 2002, “Vibrations of Rotating Cross-Ply Laminated Circular Cylindrical Shells With Stringer and Ring Stiffeners,” Int. J. Solids Struct., 39(2), pp. 529–545. [CrossRef]
Chatelet, E., Lornage, D., and Jacquet-Richardet, G., 2002, “A Three Dimensional Modeling of the Dynamic Behavior of Composite Rotors,” Int. J. Rotating Mach., 8(3), pp. 185–192. [CrossRef]
Hua, L., Khin-Yong, L., and Then-Yong, N., 2005, Rotating Shell Dynamics, Elsevier, New York.
Carrera, E., 2002, “Theories and Finite Elements for Multilayered, Anisotropic, Composite Plates and Shells,” Arch. Comput. Methods Eng., 9(2), pp. 87–140. [CrossRef]
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. [CrossRef]
Carrera, E., 2004, “Assessment of Theories for Free Vibration Analysis of Homogeneous and Multilayered Plates,” Shock Vib., 11(3–4), pp. 261–270. [CrossRef]
Carrera, E., Giunta, G., and Petrolo, M., 2011, Beam Structures. Classical and Advanced Theories, Wiley, New York.
Carrera, E., Filippi, M., and ZappinoE., 2013, “Laminated Beam Analysis by Polynomial, Trigonometric, Exponential and Zig-Zag Theories,” Eur. J. Mech. A/Solids, 41, pp. 58–69. [CrossRef]
Carrera, E., Filippi, M., and Zappino, E., 2013, “Free Vibration Analysis of Laminated Beam by Polynomial, Trigonometric, Exponential and Zig-Zag Theories,” J. Compos. Mater. (in press). [CrossRef]
Carrera, E., Filippi, M., and Zappino, E., 2013, “Analysis of Rotor Dynamic by One-Dimensional Variable Kinematic Theories,” ASME J. Gas Turbines Power, 135(9), p. 092501. [CrossRef]
Carrera, E.Filippi, M., and Zappino, E., 2013, “Free Vibration Analysis of Rotating Composite Blades Via Carrera Unified Formulation” Compos. Struct., 106, pp. 317–325. [CrossRef]
Boukhalfa, A., 2011, “Dynamic Analysis of a Spinning Laminated Composite-Material Shaft Using the HP-Version of the Finite Element Method,” Advances in Vibration Analysis Research, F. Ebrahimi, ed., InTech, Rijeka, Croatia, pp. 161–186. [CrossRef]
Viola, E., Tornabene, F., and Fantuzzi, N., 2013, “DiQuMASPAB Software,” DICAM Department, Alma Mater Studiorum, University of Bologna, Bologna, Italy, http://software.dicam.unibo.it/diqumaspab-project


Grahic Jump Location
Fig. 1

Physical and material reference systems

Grahic Jump Location
Fig. 2

Sketch of the box beam

Grahic Jump Location
Fig. 3

Dependency of frequency ratios upon the speed parameter for the cantilever box beam (R = 1): (a) θ = 0 and (b) θ = 90

Grahic Jump Location
Fig. 4

Dependency of frequency ratio upon the speed parameter for various values of ply angles (R = 1): solid line TE2, dashed line TE6

Grahic Jump Location
Fig. 5

Dependency of frequency ratio and damping upon the speed parameter for a cantilever box beam (R = 1 and case I): (a) EBBT, FSDT and (b) TE3, TE6

Grahic Jump Location
Fig. 6

Dependency of frequency and damping ratios upon the speed parameter for a cantilever box beam (R = 1 and case II): (a) EBBT, FSDT and (b) TE3, TE6

Grahic Jump Location
Fig. 7

Dependency of frequency and damping ratios upon the speed parameter for a cantilever box beam (R = 0.5): (a) lines θ = 0, bold lines θ = 15, (b) frequency ratios TE6, and (c) damping ratios TE6



Some tools below are only available to our subscribers or users with an online account.

Related Content

Customize your page view by dragging and repositioning the boxes below.

Related Journal Articles
Related eBook Content
Topic Collections

Sorry! You do not have access to this content. For assistance or to subscribe, please contact us:

  • TELEPHONE: 1-800-843-2763 (Toll-free in the USA)
  • EMAIL: asmedigitalcollection@asme.org
Sign In