Research Papers: Gas Turbines: Structures and Dynamics

Analysis of Rotor Dynamic by One-Dimensional Variable Kinematic Theories

[+] Author and Article Information
E. Carrera

Professor of Aerospace Structures
and Aeroelasticity
e-mail: erasmo.carrera@polito.it

E. M. Filippi

e-mail: matteo.filippi@polito.it

E. Zappino

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

1Corresponding author.

Contributed by the Structures and Dynamics Committee of ASME for publication in the JOURNAL OF ENGINEERING FOR GAS TURBINES AND POWER. Manuscript received December 11, 2012; final manuscript received April 29, 2013; published online July 31, 2013. Assoc. Editor: Jerzy T. Sawicki.

J. Eng. Gas Turbines Power 135(9), 092501 (Jul 31, 2013) (9 pages) Paper No: GTP-12-1481; doi: 10.1115/1.4024381 History: Received December 11, 2012; Revised April 29, 2013

In this paper, Carrera's unified formulation (CUF) is used to perform free-vibrational analyses of rotating structures. The CUF is a hierarchical formulation which offers a procedure to obtain refined structural theories that account for variable kinematic description. These theories are obtained by expanding the unknown displacement variables over the beam section axes by adopting Taylor's polynomials of N-order, in which N is a free parameter. Linear case (N = 1) permits us to obtain classical beam theories while higher order expansions could lead to three-dimensional description of dynamic response of rotors. The finite element method is used to derive the governing equations in weak form. These equations are written in terms of few fundamental nuclei, whose forms do not depend on the approximation used (N). In order to assess the new theory, several analyses are carried out and the results are compared with solutions presented in the literature in graphical and numerical form. Among the considered test cases, a rotor with deformable disk is considered and the results show the convenience of using refined models since that are able to include the in plane deformability of disks.

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Fig. 2

The variation of nondimensional natural frequencies with spinning speed parameter for a beam (Jxx, Jzz) subjected to several boundary conditions (‘lines’: Eq. (27); ‘⊙’: CUF). (a) Clamped-free, (b) clamped-supported, (c) supported-supported, (d) clamped-clamped.

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Fig. 3

The first two frequency ratios w1* and w2* as functions of the spinning speed ratio for various values of aspect-ratio (‘−’: Eq. (28); ‘+’: b/h=1; ‘×’: b/h=0.7; ‘*’: b/h=0.5; ‘□’: b/h=0.3)

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Fig. 5

The rotating structure

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Fig. 6

The variation of natural frequencies with the spinning speed for the structure of Fig. 5. (a) EBBM, (b) TE1, (c) TE2, (d) TE4, (e) TE5, and (f) TE7.

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Fig. 4

The first seven frequency ratios w1*–w7* as functions of the spinning speed ratio for aspect-ratio equal to 0.1

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Fig. 7

The variation of damping with the spinning speed for the structure of Fig. 5

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Fig. 1

Sketch of the rotating reference frame




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