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Research Papers

Dynamic Analyses of Axisymmetric Rotors Through Three-Dimensional Approaches and High-Fidelity Beam Theories

[+] Author and Article Information
M. Filippi

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

E. Carrera

Department of Mechanical and
Aerospace Engineering,
Politecnico di Torino,
Torino 10129, Italy
e-mail: erasmo.carrera@polito.it

1Corresponding author.

Contributed by the Technical Committee on Vibration and Sound of ASME for publication in the JOURNAL OF VIBRATION AND ACOUSTICS. Manuscript received February 23, 2017; final manuscript received May 11, 2017; published online August 1, 2017. Assoc. Editor: John Yu.

J. Vib. Acoust 139(6), 061008 (Aug 01, 2017) (7 pages) Paper No: VIB-17-1077; doi: 10.1115/1.4036927 History: Received February 23, 2017; Revised May 11, 2017

This paper evaluates the differences between two existing ways to derive the governing equations of axisymmetric rotors in an inertial frame of reference. According to the first approach, only a skew-symmetric gyroscopic matrix appears into the equations of motion. In the second approach, besides the gyroscopic term, a convective tensor is obtained from the kinetic energy expression. This contribution is proportional to the square of the rotational speed, and it modifies the elastic energy of the rotor. The weak form of the equations of motion has been solved using high-fidelity one-dimensional finite elements, which have been developed with the Carrera Unified Formulation (CUF). The fundamental nuclei of the gyroscopic and the convective matrices are presented in CUF form, for the first time. To highlight the differences between the two approaches, numerical simulations have been carried out on relatively simple rotor configurations, whose dynamic behaviors were already studied. The current results have been compared with the solutions presented in the literature to verify the correctness of the proposed formulation. For some structures, the results computed with the two approaches differ to a significant extent.

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References

Figures

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Fig. 1

Stodola–Green rotor

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Fig. 2

Thin-walled cylinder. Continuous lines: TE3-CUF solutions; - • -: 3D ansys solution [38]: (a) Eq. (5) without Kσ0; (b) Eq.(5); and (c) Eq. (11)

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Fig. 3

(a) Equation (5); 1D-CUF solution, ° 3D ansys solution [38] and (b) Eq. (11); 1D-CUF solution, Δ DYNROT 1(1/2)D [38]

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Fig. 4

Sketch of the clamped disk

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Fig. 5

Clamped disk. °, ansys shell solution [29]; —, Eq. (5); - - -, Eq. 11; * frequencies computed in the rotating reference frame and converted into the fixed system: (a) without centrifugal stiffening contribution and (b) with centrifugal stiffening contribution

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Fig. 6

Dimensions in meters of the rotor model

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Fig. 7

(a) Campbell diagram and (b) response amplitude computed at the loaded point (at y = 0.5 m). —, Eq. (5) without centrifugal stiffening contribution; - ◻ -, Eq. 11 with centrifugal stiffening contribution; • reference solution presented in Ref. [39].

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