ARTICLE
Stability analysis of a spinning shaft in the concentric cylinder filled with an incompressible fluid
,

,

More details
Hide details
1
School of Engineering, Anhui Agricultural University, Hefei, China

2
Anhui Province Engineering Laboratory of Intelligent Agricultural Machinery and Equipment, Hefei, China

3
Institute of Applied Mechanics, College of Science, Northeastern University, Shenyang, China

Submission date: 2023-03-07

Final revision date: 2023-06-09

Acceptance date: 2023-06-12

Online publication date: 2023-08-30

Publication date: 2023-10-30

Corresponding author
Guangding Wang

School of Engineering, Anhui Agricultural University, China

Journal of Theoretical and Applied Mechanics 2023;61(4):659-672

KEYWORDS
TOPICS
ABSTRACT
This paper deals with the stability of a spinning shaft in a concentric cylinder filled with an incompressible fluid. The steady-state momentum and continuity equations for the external fluid are established. Using Taylor expansion, the fluid forces exerted on the shaft are calculated. The shaft is in the Rayleigh model taking into account the rotary inertia and gyroscopic effects. Accordingly, the governing equation of the considered system is formulated analytically. The explicit characteristic frequency equation for the pinned-pinned spinning shaft system is then derived. Finally, the stability of the system is studied by means of characteristic value analysis.

REFERENCES (42)
1.
Abdollahi R., Firouz-abadi R.D., Rahmanian M., 2021, On the stability of rotating pipes conveying fluid in annular liquid medium, Journal of Sound and Vibration, 494, 115891.

2.
Aouadi M.A., Lakrad F., 2018, On mathematical modelling of linear flexural vibrations of spinning Rayleigh beams, Journal of Sound and Vibration, 430, 17-35.

3.
Arvin H., 2019, On parametrically excited vibration and stability of beams with varying rotating speed, Iranian Journal of Science and Technology-Transactions of Mechanical Engineering, 43, 2,177-185.

4.
Bahaadini R., Dashtbayazi M.R., Hosseini M., Khalili-Parizi Z., 2018, Stability analysis of composite thin-walled pipes conveying fluid, Ocean Engineering, 160, 311-323.

5.
Bahaadini R., Saidi A.R., 2018, Stability analysis of thin-walled spinning reinforced pipes conveying fluid in thermal environment, European Journal of Mechanics; A/Solids, 72, 298-309.

6.
Chen L.W., Ku D.M., 1990, Dynamic stability analysis of a rotating shaft by the finite element method, Journal of Sound and Vibration, 143, 1, 143-151.

7.
Dwivedi A.R., Dhiman A., Sanyal A., 2022, Stratified shear-thinning fluid flow past tandem cylinders in the presence of mixed convection heat transfer with a channel-confined configuration, Journal of Fluids Engineering, 144, 5, 051301.

8.
Ebrahimi-Mamaghani A., Forooghi A., Sarparast H., Alibeigloo A., Friswell M.I., 2021, Vibration of viscoelastic axially graded beams with simultaneous axial and spinning motions under an axial load, Applied Mathematical Modelling, 90, 131-150.

9.
ElNajjar J., Daneshmand F., 2020, Stability of horizontal and vertical pipes conveying fluid under the effects of additional point masses and springs, Ocean Engineering, 206, 106943.

10.
Firouz-Abadi R.D., Haddadpour H., 2010, The flexural instability of spinning flexible cylinder partially filled with viscous liquid, Journal of Applied Mechanics, 77, 1, 1001.

11.
Gross P., Gürgöze M., Kliem W., 1993, Bifurcation and stability analysis of a rotating beam, Quarterly of Applied Mathematics, 51, 4, 701-711.

12.
Katz R., 2001, The dynamic response of a rotating shaft subject to an axially moving and rotating load, Journal of Sound and Vibration, 246, 5, 757-775.

13.
Kern D., Jehle G., 2016, Dynamics of a rotor partially filled with a viscous incompressible fluid, PAMM, 16, 1, 279-280.

14.
Kheiri M., Païdoussis M.P., Del Pozo G.C., Amabili M., 2014, Dynamics of a pipe conveying fluid flexibly restrained at the ends, Journal of Fluids and Structures, 49, 360-385.

15.
Li C., Miao X., Qiao R., Tang Q., 2021, Modeling method of bolted joints with micro-slip features and its application in flanged cylindrical shell, Thin-Walled Structures, 164, 107854.

16.
Li Q., 2022, New approach for bearing fault diagnosis based on fractional spatio-temporal sparse low rank matrix under multichannel time-varying speed condition, IEEE Transactions on Instrumentation and Measurement, 71, 1-12.

17.
Li S.J., Liu G.M., Kong W.T., 2014, Vibration analysis of pipes conveying fluid by transfer matrix method, Nuclear Engineering and Design, 266, 78-88.

18.
Li X., Qin Y., Li Y. H., Zhao X., 2018, The coupled vibration characteristics of a spinning and axially moving composite thin-walled beam, Mechanics of Advanced Materials and Structures, 25, 9, 722-731.

19.
Liang F., Gao A., Yang X.D., 2020, Dynamical analysis of spinning functionally graded pipes conveying fluid with multiple spans, Applied Mathematical Modelling, 83, 454-469.

20.
Liang F., Yang X.D., Qian Y.J., Zhang W., 2018, Transverse free vibration and stability analysis of spinning pipes conveying fluid, International Journal of Mechanical Sciences, 137, 195-204.

21.
Manchi V., Sujatha C., 2021, Torsional vibration reduction of rotating shafts for multiple orders using centrifugal double pendulum vibration absorber, Applied Acoustics, 174, 107768.

22.
Michaelides E.E., Feng Z.G., 2023, Drag coefficients of non-spherical and irregularly-shaped particles, Journal of Fluids Engineering, 145, 6, 1-74.

23.
Oyelade A.O., Oyediran A.A., 2020, Imperfect bifurcation and chaos of slightly curved carbon nanotube conveying hot pressurized fluid resting on foundations, Journal of Fluids Engineering, 142, 11.

24.
Païdoussis M.P., Issid N.T., 1974, Dynamic stability of pipes conveying fluid, Journal of Sound and Vibration, 33, 3, 267-294.

25.
Qian Q., Wang L., Ni Q., 2009, Instability of simply supported pipes conveying fluid under thermal loads, Mechanics Research Communications, 36, 3, 413-417.

26.
Saeed N.A., 2019, On vibration behavior and motion bifurcation of a nonlinear asymmetric rotating shaft, Archive of Applied Mechanics, 89, 9, 1899-1921.

27.
Sahebnasagh M., Nikkhah-Bahrami M., Firouz-Abadi R.D., 2018, Effect of multiphase fluid and functionally graded density fluid on the stability of spinning partially-filled shells, International Journal of Mechanical Sciences, 140, 109-118.

28.
Shahgholi M., Khadem S.E., Bab S., 2014, Free vibration analysis of a nonlinear slender rotating shaft with simply support conditions, Mechanism and Machine Theory, 82, 128-140.

29.
Sheu G.J., Yang S.M., 2005, Dynamic analysis of a spinning Rayleigh beam, International Journal of Mechanical Sciences, 47, 157-169.

30.
Tao M.D., Zhang W., 2002, Dynamic stability of a flexible spinning cylinder partially filled with liquid, Journal of Applied Mechanics, 69, 5, 708-710.

31.
Wang G.D., Yuan H.Q., 2018, An analysis of dynamic stability for a flexible rotor filled with liquid, Physics of Fluids, 30, 3, 037101.

32.
Wang G., Yuan H., 2019a, Dynamic stability analysis of a flexible rotor filled with liquid based on three-dimensional flow, Journal of Fluids Engineering, 141, 5.

33.
Wang G.D., Yuan H.Q., 2019b, Stability analysis of a flexible rotor partially filled with two liquid phases, Physics of Fluids, 31, 017103.

34.
Wang G.D., Yuan H.Q., 2021, Dynamics and stability analysis of an axially functionally graded hollow rotor partially filled with liquid, Composite Structures, 266, 113821.

35.
Wang H.F., Chen C., 2020, Stability analysis of a rotor system with fluid applying wave resonance theory, Physics of Fluids, 32, 5, 054106.

36.
Wang H.F., Chen G., Jiang G.Y., 2021, Stability analysis of an anisotropic rotor partially filled with viscous incompressible fluid based on Andronov-Hopf bifurcation, Physics of Fluids, 33, 6, 064111.

37.
Yang S., Hu H., Mo G., Zhang X., Qin J., Yin S., Zhang J., 2021, Dynamic modeling and analysis of an axially moving and spinning Rayleigh beam based on a time-varying element, Applied Mathematical Modelling, 95, 409-434.

38.
Zhang Y., Yang X., Zhang W., 2020a, Modeling and stability analysis of a flexible rotor based on the Timoshenko beam theory, Acta Mechanica Solida Sinica, 33, 3, 281-293.

39.
Zhang J.W., Zhu L., Chen P.,Wu Q.M.,Wei M., Yin C.L., Li G.L., 2020b, Flowing interaction between cutting edge of ploughbreast with soil in shifting tillage operations, Engineering Applications of Computational Fluid Mechanics, 14, 1, 1404-1415.

40.
Zhou X.W., Dai H.L., Wang L., 2018, Dynamics of axially functionally graded cantilevered pipes conveying fluid, Composite Structures, 190, 112-118.

41.
Zhu K., Chung J., 2019, Vibration and stability analysis of a simply-supported Rayleigh beam with spinning and axial motions, Applied Mathematical Modelling, 66, 362-382.

42.
Zhu L., Luo F., Qi Y.Y., Wei M., Ge J.R., Liu W.L., Li G.L., Jen T.C., 2018, Effects of spray angle variation on mixing in a cold supersonic combustor with kerosene fuel, Acta Astronautica, 144, 1-11.

 eISSN: 2543-6309 ISSN: 1429-2955