Flapwise bending vibration analysis of a rotating double-tapered Timoshenko beam

Archive of Applied Mechanics

Volumn 78, Issue 5, 2008, Pages 379-392

  Ozdemir Ozgumus, O ^a   Kaya, M O ^a  

^a ISTANBUL TECHNICAL UNIVERSITY   (Turkey)

Author keywords

Differential transform method; Differential transformation; Nonuniform Timoshenko beam; Rotating Timoshenko beam; Tapered Timoshenko beam

Indexed keywords

BOUNDARY CONDITIONS; EULER EQUATIONS; KINETIC ENERGY; NATURAL FREQUENCIES; POTENTIAL ENERGY; PROBLEM SOLVING;

DIFFERENTIAL TRANSFORM METHOD; NONUNIFORM TIMOSHENKO BEAM; ROTATING TIMOSHENKO BEAM; TAPERED TIMOSHENKO BEAM;

VIBRATION ANALYSIS;

EID: 43449110163     PISSN: 09391533     EISSN: 14320681     Source Type: Journal    
DOI: 10.1007/s00419-007-0158-5     Document Type: Article

References (22)

1. Banerjee J.R. (2001). Dynamic stiffness formulation and free vibration analysis of centrifugally stiffened Timoshenko beams. J. Sound Vib. 247(1): 97-115
2. Banerjee J.R. and Williams F.W. (1985). Exact Bernoulli-Euler dynamic stiffness matrix for a range of tapered beams. Int. J. Numer. Methods Eng. 21: 2289-2302
3. Bazoune A. and Khulief Y.A. (1992). A finite beam element for vibration analysis of rotating tapered Timoshenko beams. J. Sound Vib. 156: 141-164
4. Downs B. (1977). Transverse vibrations of cantilever beam having unequal breadth and depth tapers. ASME J. Appl. Mech. 44: 737-742
5. Eringen A.C. (1980). Mechanics of continua. Robert E. Krieger, Huntington
6. Grossi R.O. and Bhat R.B. (1991). A note on vibrating tapered beams. J. Sound Vib. 147: 174-178
7. Hodges, D.H., Dowell, E.H.: Nonlinear equations of motion for the elastic bending and torsion of twisted nonuniform rotor blades. NASA TN D-7818 (1974)
8. Kaya M.O. (2006). Free vibration analysis of rotating Timoshenko beams by differential transform method. Aircr. Eng. Aerosp. Tech. 78(3): 194-203
9. Khulief Y.A. and Bazoune A. (1992). Frequencies of rotating tapered Timoshenko beams with different boundary conditions. Comput. Struct. 42: 781-795
10. Kim C.S. and Dickinson S.M. (1988). On the analysis of laterally vibrating slender beams subject to various complicating effects. J. Sound Vib. 122: 441-455
11. Klein L. (1974). Transverse vibrations of non-uniform beam. J. Sound Vib. 37: 491-505
12. Lau J.H. (1984). Vibration frequencies of tapered bars with end mass. ASME J. Appl. Mech. 51: 179-181
13. Lee S.Y. and Kuo Y.H. (1992). Exact solution for the analysis of general elastically restrained non-uniform beams. ASME J. Appl. Mech. 59: 205-212
14. Lee S.Y. and Lin S.M. (1994). Bending vibrations of rotating non-uniform Timoshenko beams with an elastically restrained root. J. Appl. Mech. 61: 949-955
15. Lee S.Y., Ke H.Y. and Kuo Y.H. (1990). Analysis of non-uniform beam vibration. J. Sound Vib. 142: 15-29
16. Naguleswaran S. (1994). Vibration in the two principal planes of a non-uniform beam of rectangular cross-section, one side of which varies as the square root of the axial co-ordinate. J. Sound Vib. 172: 305-319
17. Ozdemir Ozgumus O. and Kaya M.O. (2006). Flexural vibration analysis of double tapered rotating Euler-Bernoulli beam by using the differential transform method. Meccanica 41(6): 661-670
18. Özdemir Ö. and Kaya M.O. (2006). Flapwise bending vibration analysis of a rotating tapered cantilevered Bernoulli-Euler beam by differential transform method. J. Sound Vib. 289: 413-420
19. Storti D. and Aboelnaga Y. (1987). Bending vibration of a class of rotating beams with hypergeometric solutions. ASME J. Appl. Mech. 54: 311-314
20. Swaminathan M. and Rao J.S. (1977). Vibrations of rotating, pretwisted and tapered blades. Mech. Mach. Theory 12: 331-337
21. To C.W.S. (1979). Higher order tapered beam finite elements for vibration analysis. J. Sound Vib. 63: 33-50
22. Williams F.W. and Banerjee J.R. (1985). Flexural vibration of axially loaded beams with linear or parabolic taper. J. Sound Vib. 99: 121-138