Nonlinear Flapping-Torsional Free Vibration Analysis of Rotating Beams Considering the Coriolis Force

Document Type : Research Article

Author

Department of Mechanical Engineering, Faculty of Engineering, Shahrekord University

Abstract

The nonlinear free flapping-torsional vibration of rotating beams is investigated in this paper. The presented equations are based on the exact geometrical formulation in conjunction with the Cosserat theory for rods. The equations of motion are reduced to the flapping and torsional equations of motion for symmetric rectangular beams by neglecting the shear deformation. The governing equations are coupled to each other with the non-homogenous boundary conditions. By employing the direct method of multiple scales the effective nonlinearity coefficients of nonlinear natural frequencies are extracted. After validation of the current results, the effects of the rotating speed on the type and the value of the effective nonlinearity coefficient of natural frequencies are examined. The sign of the effective nonlinearity coefficient demonstrates the softening or hardening treatment of the corresponding nonlinear natural frequencies. It is concluded that ignoring the flapping-torsional coupling due to the Coriolis force, for odd modes makes some errors in the magnitude of effective nonlinearity but the type of nonlinearity is predicted correctly. On the other hand, in the even modes for average to high rotation speed in addition to incorrect estimation of the magnitude of effective nonlinearity the different type of nonlinearity is also predicted.

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References

[1] D.H. Hodges, E. Dowell, Nonlinear equations of motion for the elastic bending and torsion of twisted nonuniform rotor blades, NASA TN D-7818, (1974).
[2] M.C. Da Silva, D. Hodges, Nonlinear flexure and torsion of rotating beams, with application to helicopter rotor blades-I. Formulation, Vertica, 10(2) (1986) 151-169.
[3] M.C. da Silva, D. Hodges, Nonlinear flexure and torsion of rotating beams, with application to helicopter rotor blades-II. Response and stability results, Vertica, 10(2) (1986) 171-186.
[4] D.H. Hodges, A mixed variational formulation based on exact intrinsic equations for dynamics of moving beams, International journal of solids and structures, 26(11) (1990) 1253-1273.
[5] D.H. Hodges, Comment on 'Flexural behavior of a rotating sandwich tapered beam' and on 'Dynamic analysis for free vibrations of rotating sandwich tapered beams', AIAA journal, 33(6) (1995) 1168-1170.
[6] K. Avramov, C. Pierre, N. Shyriaieva, Nonlinear equations of flexural-flexural-torsional oscillations of rotating beams with arbitrary cross-section, International Applied Mechanics, 44(5) (2008) 582-589.
[7] J. Valverde, D. García-Vallejo, Stability analysis of a substructured model of the rotating beam, Nonlinear dynamics, 55(4) (2009) 355-372.
[8] W. Lacarbonara, H. Arvin, F. Bakhtiari-Nejad, A geometrically exact approach to the overall dynamics of elastic rotating blades—part 1: linear modal properties, Nonlinear Dynamics, 70(1) (2012) 659-675.
[9] H. Arvin, W. Lacarbonara, F. Bakhtiari-Nejad, A geometrically exact approach to the overall dynamics of elastic rotating blades—part 2: flapping nonlinear normal modes, Nonlinear Dynamics, 70(3) (2012) 2279-2301.
[10] H. Arvin, W. Lacarbonara, A fully nonlinear dynamic formulation for rotating composite beams: nonlinear normal modes in flapping, Composite structures, 109 (2014) 93-105.
[11] Ö. Turhan, G. Bulut, On nonlinear vibrations of a rotating beam, Journal of sound and vibration, 322(1-2) (2009) 314-335.
[12] H. Arvin, F. Bakhtiari-Nejad, Non-linear modal analysis of a rotating beam, International Journal of Non-Linear Mechanics, 46(6) (2011) 877-897.
[13] W. Lacarbonara, Nonlinear structural mechanics: theory, dynamical phenomena and modeling, Springer Science & Business Media, 2013.
[14] A.H. Nayfeh, D.T. Mook, Nonlinear oscillations, John Wiley & Sons, 2008.
[15] L. Meirovitch, Principles and techniques of vibrations, Prentice Hall New Jersey, 1997.
[16] H. Arvin, F. Bakhtiari-Nejad, Nonlinear free vibration analysis of rotating composite Timoshenko beams, Composite Structures, 96 (2013) 29-43.
 
Amirkabir Journal of Mechanical Engineering
Volume 52, Issue 12
March 2021
Pages 3445-3462

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