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Research Papers

Vibration Analysis of Thin/Thick, Composites/Metallic Spinning Cylindrical Shells by Refined Beam Models

[+] Author and Article Information
E. Carrera

Professor of Aerospace Structures
and Aeroelasticity,
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,
124 La Trobe Street,
Melbourne 3000, 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 Technical Committee on Vibration and Sound of ASME for publication in the JOURNAL OF VIBRATION AND ACOUSTICS. Manuscript received March 31, 2014; final manuscript received January 28, 2015; published online March 13, 2015. Assoc. Editor: Yukio Ishida.

J. Vib. Acoust 137(3), 031020 (Jun 01, 2015) (9 pages) Paper No: VIB-14-1115; doi: 10.1115/1.4029688 History: Received March 31, 2014; Revised January 28, 2015; Online March 13, 2015

This paper evaluates the vibration characteristics of thin/thick rotating cylindrical shells made of metallic and composite materials. A previous theory of the authors is extended here to include the effects of geometrical stiffness due to rotation. To this end, variable kinematic one-dimensional (1D) models obtained by applying the Carrera Unified Formulation (CUF) were used. The components of the displacement fields are x, z polynomials of arbitrary order N, making it possible to go beyond the rigid cross section assumptions of the classical beam theories. A significant contribution of this formulation consists in the possibility to include the in-plane cross-sectional deformations allowing the introduction of the in-plane initial stress effects, e.g., the effect of the geometrical stiffness. Equations of motions, including both Coriolis and in-plane initial stress contributions, were solved through the finite element method. Several analyses were carried out on both thin and thick cylinders made of either metallic or composite materials with different boundary conditions. The results are compared with analytical and numerical shell formulations and three-dimensional solutions available in the literature. Various laminate lay-up have been considered in the case of composites shells. Numerical evaluations of the effect of geometric stiffness are provided, demonstrating its importance in the analyses presented. The 1D models appear very effective to investigate the dynamics of spinning shells and, contrary to shell theories, they do not require any amendments with thick shell geometry. From the computational point of view, the present refined beam models are less expensive than the shell and solid counterparts.

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References

Figures

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Fig. 1

Physical and material coordinate reference systems

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Fig. 2

Dependency of frequency ratio upon the speed parameter for various TE expansions

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Fig. 3

Dependency of frequency ratio upon the speed parameter. “—”: Eq. (19), “– – –”: Eq. (20), “- - -”: Eq. (21), “●”: Ref. [7] of Ref. [11], “⋯”: TE7 w/o σ0: ‐·‐. (a) Supported–supported and (b) clamped–clamped.

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Fig. 4

Dependency of frequency ratio upon the speed parameter. “—”: Eq. (19), “– – –”: Eq. (20), “- - -”: Eq. (21), “●”: Ref. [7] of Ref. [11], “⋯”: TE7 w/o σ0: ‐·‐. (a) k = 5 and n = 3; (b) k = 3 and n = 4.

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Fig. 5

Dependency of frequency ratio upon the speed parameter. “--●--”: Ref. [14] and “—”: TE7 (α = 0.02 and k = 0.5)

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Fig. 6

Dependency of frequency ratio upon the speed parameter of axial bending and global bending modes. TE9, n = 1, and Ref. [15].

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Fig. 7

Dependency of frequency ratio upon the speed parameter of pure radial (m = 0) and radial shearing modes (m = 1, 2). TE9. (a) n = 2 and (b) n = 3.

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Fig. 8

Dependency of frequency ratio upon the speed parameter of extensional (n = 0, 2 and m = 0) and global torsion modes (n = 0, m = 0) TE9, Ref. [15]

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Fig. 9

Dependency of the frequency ratios upon the speed parameter for two different longitudinal wave number. TE8. “-+-”: (0 deg/0 deg), “-×-”: (30 deg/30 deg), “-*-”: (45 deg/45 deg), “-□-”: (65 deg/65 deg), “-▪-”: (90 deg/90 deg), and “-∘-”: (0 deg/90 deg/0 deg). (a) n = 1 and m = 1; (b) n = 1 and m = 2.

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Fig. 10

Dependency of the frequency ratios upon the speed parameter for two different circumferential wave number. TE8. “-+-”: (0 deg/0 deg), “-×-”: (30 deg/30 deg), “-*-”: (45 deg/45 deg), “-□-”: (65 deg/65 deg), “-▪-”: (90 deg/90 deg), and “-∘-”: (0 deg/90 deg/0 deg). (a) n = 2 and m = 1; (b) n = 3 and m = 1.

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Fig. 11

Dependency of the frequency ratios upon the speed parameter for the torsional mode. TE8, n = 1, m = 0. “-+-”: (0 deg/0 deg), “-×-”: (30 deg/30 deg), “-*-”: (45 deg/45 deg), “-□-”: (65 deg/65 deg), “-▪-”: (90 deg/90 deg), and “-∘-”: (0 deg/90 deg/0 deg).

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