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Research Papers

Specific Features of Dynamic Behavior of Stationary and Rotating Single/Coaxial Cylindrical Shells Interacting With the Axial and Rotational Fluid Flows

[+] Author and Article Information
Sergey A. Bochkarev

Institute of Continuous Media Mechanics RAS,
Acad. Korolev Str 1,
Perm 614013, Russia
e-mail: bochkarev@icmm.ru

Valery P. Matveenko

Institute of Continuous Media Mechanics RAS,
Acad. Korolev Str 1,
Perm 614013, Russia

1Corresponding author.

Contributed by the Technical Committee on Vibration and Sound of ASME for publication in the JOURNAL OF VIBRATION AND ACOUSTICS. Manuscript received May 22, 2013; final manuscript received October 13, 2014; published online November 14, 2014. Assoc. Editor: Massimo Ruzzene.

J. Vib. Acoust 137(2), 021001 (Apr 01, 2015) (10 pages) Paper No: VIB-13-1176; doi: 10.1115/1.4028829 History: Received May 22, 2013; Revised October 13, 2014; Online November 14, 2014

The paper is concerned with the finite element analysis of hydroelastic stability of stationary or rotating elastic single and coaxial cylindrical shells subjected to compressible fluid flows having axial and tangential velocity components. The behavior of the flowing and rotating fluid is described in the framework of the potential theory. Consideration of elastic shells is based on the classical shell model. The results of the numerical analysis of shell stability for various boundary conditions, geometrical dimensions and different sizes of the annular gap between the outer and inner shells are discussed. It has been found that single and coaxial shells interacting with the combined fluid flows show qualitative differences in the dynamic behavior.

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Figures

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Fig. 1

Computational scheme

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Fig. 5

The real λ1 and imaginary λ2 parts of eigenvalues (Hz) versus the angular velocity of the rotating shell and corotating fluid Ω (rad/s) for shells simply supported at both ends: (a) configuration 1, Ω=Ωsi=Ωfi; (b) configuration 3, Ω=Ωso=Ωfo≠0,Ωfi=0; forward waves—solid lines; backward waves—dashed lines; imaginary parts—dashed-dotted lines

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Fig. 7

Stability diagram for coaxial shells with different boundary conditions under the combined action of the axial flow Uo (m/s) and rotational flow with the angular velocity Ωfo (rad/s): configuration 3; j = 3; (a) k = 1/2; (b) k = 1/10; SS—simply supported shells; CC—clamped shells; CF—cantilevered shells

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Fig. 2

Variation of the forward (solid lines) and backward (dashed lines) modes of low-frequency vibrations λ1 (Hz) with the angular velocity Ωs (rev/s) of an empty shell with free end-clamped end boundary conditions at m = 1 for two harmonics: lines correspond to the results of calculations; symbols denote the results obtained in Guo et al. [28]

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Fig. 3

Variation of the real parts Ξo1 of dimensionless eigenvalues with dimensionless axial velocity of the annular flow Λo for clamped coaxial shells; k = 1/10, j = 3; lines—the results of our calculations; symbols—the results of Païdoussis et al. [16]; antisymmetric modes—solid lines and open symbols; symmetric modes—dashed lines and closed symbols

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Fig. 4

The real λ1 and imaginary λ2 parts of eigenvalues (Hz) versus the angular velocity (rad/s) of the internal Ωfi and annular Ωfo flows for stationary shells simply supported at both ends: (a) configuration 1; (b) configuration 3; forward waves—solid lines; backward waves—dashed lines; imaginary parts—dashed-dotted lines

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Fig. 6

Stability diagram for shells with different boundary conditions under the combined action of the axial flow Ui (m/s) and rotational flow with the angular velocity Ωfi (rad/s): configuration 2; j = 4; (a) L/R = 4; (b) L/R = 10; SS—simply supported shells; CC—clamped shells; CF—cantilevered shells

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Fig. 8

Stability diagram of the system under the combined action of the axial flow Ui (m/s) and simultaneous rotation of the shell and the fluid Ω=Ωsi=Ωfi (rad/s) for shells with various boundary conditions: configuration 2; j = 4; (a) L/R = 4; (b) L/R = 10; SS—simply supported shells; CC—clamped shells; CF—cantilevered shells

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Fig. 9

Stability diagram for coaxial shells with various boundary conditions under the combined action of the axial flow Uo (m/s) and simultaneous rotation of the shell and the fluid with the angular velocity Ω=Ωso=Ωfo≠0,Ωfi=0 (rad/s): configuration 3; j = 3; (a) k = 1/2; (b) k = 1/10; SS—simply supported shells; CC—clamped shells; CF—cantilevered shells

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