Free vibration and wave propagation analysis of uniform and tapered rotating beams using spectrally formulated finite elements

International Journal of Solids and Structures

Volumn 44, Issue 18-19, 2007, Pages 5875-5893

  Vinod, K G ^a   Gopalakrishnan, S ^a   Ganguli, Ranjan ^a  

^a INDIAN INSTITUTE OF SCIENCE   (India)

Author keywords

Dynamic stiffness matrix; Functional; Lagrangian; Non dispersive; Spectrum relation; Transfer function; Wavenumber

Indexed keywords

CENTRIFUGAL FORCES; ROTATING BEAMS; WAVENUMBER;

COMPUTATIONAL METHODS; DIFFERENTIAL EQUATIONS; FINITE ELEMENT METHOD; LAGRANGE MULTIPLIERS; SPECTRUM ANALYSIS; STIFFNESS MATRIX; TRANSFER FUNCTIONS; WAVE PROPAGATION;

BEAMS AND GIRDERS;

EID: 34447503848     PISSN: 00207683     EISSN: None     Source Type: Journal    
DOI: 10.1016/j.ijsolstr.2007.02.002     Document Type: Article

References (36)

1. Banerjee J.R. Free vibration of centrifugally stiffened uniform and tapered beams using the dynamic stiffness method. Journal of Sound and Vibration 233 5 (2000) 857-875
2. Boyce W.E. Effect of hub radius on the vibration of uniform bar. Journal of Applied Mechanics 23 2 (1956) 287-290
3. Cesnik C.E.S., and Shin S. On the modeling of integrally actuated helicopter blades. International Journal of Solids and Structures 38 10-13 (2001) 1765-1789
4. Chakraborty A., and Gopalakrishnan S. A spectrally formulated finite element for wave propagation analysis in functionally graded beams. International Journal of Solids and Structures 40 (2003) 2421-2448
5. Chakraborty A., and Gopalakrishnan S. A spectral finite element for axial-flexural-shear coupled wave propagation analysis in lengthwise graded beam. Computational Mechanics 36 (2005) 1-12
6. Chakraborty A., Sivakumar M.S., and Gopalakrishnan S. Spectral element based model for wave propagation analysis in multi-wall carbon nanotubes. International Journal of Solids and Structures 43 2 (2006) 279-294
7. Cheng J., and Xu H. Inner mass impact damper for attenuating structure vibration. International Journal of Solids and Structures 43 17 (2006) 5355-5369
8. Chung J., and Yoo H.H. Dynamic analysis of a rotating cantilever beam by using the finite element method. Journal of Sound and Vibration 249 1 (2002) 147-164
9. Datta P.K., and Ganguli R. Vibration characteristics of rotating gas turbine blades with localized damage including the effects of shear deformation and rotary inertia. Computers and Structures 36 6 (1990) 1129-1133
10. Doyle J.F. A spectrally formulated finite element for longitudinal wave propagation. International Journal of Analytical and Experimental Modal Analysis 5 (1988) 99-107
11. Doyle J.F. Wave Propagation in Structures: An FFT Based Spectral Analysis Methodology (1989), Springer-Verlag, New York
12. Doyle J.F., and Farris T.N. A spectrally formulated element for flexural wave propagation in beams. International Journal of Analytical and Experimental Modal Analysis 3 (1990) 1-5
13. Fox C.H.J., and Burdess J.S. The natural frequencies of a thin rotating cantilever with offset root. Journal of Sound and Vibration 65 (1979) 151-158
14. Gopalakrishnan S., and Doyle J.F. Wave propagation in connected waveguides of varying cross-section. Journal of Sound and Vibration 175 3 (1994) 347-363
15. Gopalakrishnan S., Martin M., and Doyle J.F. A matrix methodology for spectral analysis of wave propagation in multiple connected Timoshenko beams. Journal of Sound and Vibration 158 l (1992) 11-24
16. Gudla P.K., and Ganguli R. Discontinuous Galerkin finite element in time for solving periodic differential equations. Computer Methods in Applied Mechanics and Engineering 196 1-3 (2006) 682-696
17. Hodges D.H. Vibration response of non-uniform rotating beams with discontinuities. Journal of the American Helicopter Society 24 5 (1979) 43-50
18. Hodges D.H., and Rutkowski M.J. Free-vibration analysis of rotating beams by a variable-order finite element method. AIAA Journal 19 11 (1981) 1459-1466
19. Hunter,W.F., 1970. Integrating matrix method for determining the natural vibration characteristics of propeller blades. NASA TN D-6064.
20. Lawther R. Assessing how changes to a structure can create gaps in the natural frequency spectrum. International Journal of Solids and Structures 44 2 (2007) 614-635
21. Lee U., and Oh H. Dynamics of an axially moving viscoelastic beam subject to axial tension. International Journal of Solids and Structures 42 8 (2005) 2381-2398
22. Martin M., Gopalakrishanan S., and Doyle J.F. Wave propagation in multiply connected deep wave guides. Journal of Sound and Vibration 174 4 (1994) 521-538
23. Naguleswaran N. Lateral vibration of a centrifugally tensioned uniform Euler-Bernoulli beam. Journal of Sound and Vibration 176 5 (1994) 613-624
24. Narayanan G.V., and Beskos D.E. Numerical operational methods for time-dependant linear problems. International Journal for Numerical Methods in Engineering 18 (1982) 1829-1854
25. Pawar P.M., and Ganguli R. On the effect of progressive damage on composite helicopter rotor system behavior. Composite Structures 78 3 (2007) 410-423
26. Pnueli D. Natural bending frequency comparable to rotational frequency in rotating cantilever beam. Journal of Applied Mechanics 39 2 (1972) 604-606
27. Putter S., and Manor H. Natural frequencies of radial rotating beams. Journal of Sound and Vibration 56 (1978) 175-185
28. Rossing T.D., and Fletcher N.H. Principles of Vibration and Sound (1995), Springer-Verlag, New York
29. Roy N., and Ganguli R. Helicopter rotor blade frequency evolution with damage growth and signal processing. Journal of Sound and Vibration 283 3-5 (2005) 821-851
30. Roy Mahapatra D., and Gopalakrishnan S. A spectral finite element model for analysis of axial-flexural-shear coupled wave propagation in laminated composite beams. Composite Structures 59 (2003) 67-88
31. Roy Mahapatra D., Gopalakrishnan S., and Sankar T.S. Spectral-element-based solutions for wave propagation analysis of multiply connected unsymmetric laminated composite beams. Journal of Sound and Vibration 237 5 (2000) 819-836
32. Stephen N.G., and Zhang Y. Eigen analysis and continuum modeling of pre-twisted repetitive beam-like structures. International Journal of Solids and Structures 43 13 (2006) 3832-3855
33. Thakkar D., and Ganguli R. Dynamic response of rotating beams with piezoceramic actuation. Journal of Sound and Vibration 270 4-5 (2004) 729-753
34. Vinod K.G., Gopalakrishnan S., and Ganguli R. Wave propagation characteristics of rotating Euler-Bernoulli beams. Computer Modeling in Engineering and Sciences 16 3 (2006) 197-208
35. Wang G., and Wereley N.M. Free vibration analysis of rotating blades with uniform tapers. AIAA Journal 42 12 (2004) 2429-2437
36. Wright A.D., Smith C.E., Thresher R.W., and Wang J.L.C. Vibration modes of centrifugally stiffened beams. Journal of Applied Mechanics 49 2 (1982) 197-202