Nonlinear equations of flexural-flexural-torsional oscillations of rotating beamswith arbitrary cross-section

International Applied Mechanics

Volumn 44, Issue 5, 2008, Pages 582-589

  Avramov, K V ^a   Pierre, C ^b   Shyriaieva, N V ^a  

^a NATIONAL TECHNICAL UNIVERSITY   (Ukraine)

^b UNIVERSITÉ DE MONTRÉAL   (Canada)

Author keywords

Cross section; Flexural flexural torsional vibrations; Rotating beam

Indexed keywords

ARBITRARY CROSS SECTIONS; CENTER-OF-GRAVITY; CROSS-SECTION; FLEXURAL-FLEXURAL-TORSIONAL VIBRATIONS; FLEXURAL-TORSIONAL; FLEXURAL-TORSIONAL VIBRATIONS; HAMILTON'S PRINCIPLE; NON-LINEAR PARTIAL DIFFERENTIAL EQUATIONS; ROTATING BEAM; SHEAR CENTER;

DIFFERENCE EQUATIONS; DIFFERENTIAL EQUATIONS; DIFFERENTIATION (CALCULUS); NONLINEAR EQUATIONS; ROTATION; VIBRATIONS (MECHANICAL);

PARTIAL DIFFERENTIAL EQUATIONS;

EID: 53149107052     PISSN: 10637095     EISSN: 15738582     Source Type: Journal    
DOI: 10.1007/s10778-008-0071-9     Document Type: Article

References (16)

1. M. R. M. Crespo da Silva C. C. Glynn 1978 Nonlinear flexural-flexural- torsional dynamics of inextensional beams. I: Equations of motion J. Struct. Mech. 6 4 437 448
2. M. R. M. Crespo da Silva C. C. Glynn 1978 Nonlinear flexural-flexural- torsional dynamics of inextensional beams. II: Forced motions J. Struct. Mech. 6 4 449 461
3. M. R. M. Crespo da Silva 1998 A comprehensive analysis of the dynamics of a helicopter rotor blade Int. J. Solids Struct. 35 7-8 619 635
4. M. R. M. Crespo da Silva 1988 Nonlinear flexural-flexural-torsional- extensional dynamics of beams. I: Formulation Int. J. Solids Struct. 24 12 1225 1234
5. G. Y. Dzanelidze, "On the theory of thin and thin-walled rods," National Advisory Committee for Aeronautics, NACA TM 1309, Washington (1951).
6. A. P. Filippov, Vibrations of Deformable Systems [in Russian], Mashinostroenie, Moscow (1970).
7. P. P. Friedmann 1980 Aeroelastic stability and response analysis of large horizontal-axis wind turbines J. Industr. Aerodynam. 5 373 401
8. D. H. Hodges and E. H. Dowell, Nonlinear Equations of Motion for the Elastic Bending and Torsion of Twisted Nonuniform Rotor Blades, NASA TN D-7818, Washington (1974).
9. A. H. Nayfeh and P. F. Pai, Linear and Nonlinear Structural Mechanics, Wiley & Sons, New York (2004).
10. S. P. Timoshenko and D. H. Young, Vibration Problems in Engineering, Van Nostrand, Princeton, NJ (1955).
11. S. W. Shaw C. Pierre E. Pesheck 1999 Modal analysis-based reduced-order models for nonlinear structures: An invariant manifolds approach The Shock and Vibration Digest 31 3 16
12. K. V. Avramov C. Pierre N. V. Shyriaieva 2006 Nonlinear normal vibrations modes of systems with gyroscopic terms Dokl. NAN Ukrainy 11 7 10
13. K. V. Avramov Yu. V. Mikhlin 2005 Damping of free elastic vibrations in linear systems Int. Appl. Mech. 41 2 203 209
14. K. V. Avramov 2006 Nonlinear forced vibrations of a cylindrical shell with two internal resonances Int. Appl. Mech. 42 2 169 175
15. K. V. Avramov 2006 Chaotic frictional vibrations excited by a quasiperiodic load Int. Appl. Mech. 42 9 1071 1076
16. Yu. V. Mikhlin S. N. Reshetnikova 2005 Dynamic analysis of a two-mass system with essentially nonlinear vibration damping Int. Appl. Mech. 41 1 77 84