Large amplitude free vibration analysis of a rotating beam with non-linear spring and mass system

JVC/Journal of Vibration and Control

Volumn 11, Issue 12, 2005, Pages 1511-1533

  Das, S K ^a   Ray, P C ^a   Pohit, G ^b  

^a GOVERNMENT COLLEGE OF ENGINEERING AND LEATHER TECHNOLOGY   (India)

^b JADAVPUR UNIVERSITY   (India)

Author keywords

Large amplitude vibration; Multi time scale analysis; Non linear spring mass system; Non linear vibration; Rotating beam

Indexed keywords

BOUNDARY CONDITIONS; CONSTRAINT THEORY; NONLINEAR SYSTEMS; PARTIAL DIFFERENTIAL EQUATIONS;

LARGE AMPLITUDE VIBRATION; MULTI TIME-SCALE ANALYSIS; NON-LINEAR SPRING-MASS SYSTEM; NON-LINEAR VIBRATION; ROTATING BEAM;

VIBRATION CONTROL;

EID: 29144534105     PISSN: 10775463     EISSN: None     Source Type: Journal    
DOI: 10.1177/1077546305060767     Document Type: Review

References (25)

1. Anderson, G. L., 1975, "On the extensional and flexural vibrations of rotating bars," International Journal for Non-linear Mechanics 10, 223-236.
2. Bauchau, O. A., 1985, "A beam theory for anisotropic materials," Journal of Applied Mechanics 52, 416-422.
3. Bousman, W. G., Ormiston, R. A., and Mirick, P. H., 1983, "Design considerations for the bearingless rotor hubs," in Proceedings of the 39th Annual Forum of the American Helicopter Society, St. Louis, MO.
4. Felkar, F., Lan, B., McLaughlin, S., and Johnson, W., 1987, "Non-linear behavior of an elastomeric lag damper undergoing dual-frequency motion and its effect on rotor dynamics," Journal of the American Helicopter Society 34(4), 45-53.
5. Friedmann, P., Yuan, K., Millott, T., and Venkatesan, C., 1994, "Correlation studies for hingless rotors in forward flight," in Proceedings of the AIAA Dynamics Specialists Conference, Hilton Head, SC, AIAA 94-1722.
6. Gandhi, F. and Chopra, I., 1996, "Analysis of bearingless main rotor dynamics with the inclusion of an improved time domain non-linear elastomeric model," Journal of the American Helicopter Society 41(3), 267-277.
7. Gupta, P. K., Venkatesan, C., and Singh, O., 1997, "Structural dynamics of rotor blades with precone-presweeppredoor-pretwist and torque offset including hub motion," in Proceedings of the 48th ACM, Aeronautical Society of India, Khragpur, India.
8. Hodges, D. H. and Dowell, E. H., 1974, "Non-linear equations of motion for the elastic bending and torsion of twisted non-uniform rotor blades," NASA TN D-7818.
9. Housmann, G., 1986, "Structural analysis and design considerations of elastomeric dampers with viscoelastic material behavior." in Proceedings of the 12th European Rotorcraft Forum, Garmisch-Partenkirchen, Germany, Sepember, pp. 70.1-70.26.
10. Huber, H., 1992, "Will rotor hubs lose their bearings? A survey of bearingless main rotor development," in Proceedings of the 18th European Rotorcraft Forum, Avignon, France.
11. Kaza, K. R. and Kvatemik, R. G., 1977, "Non-linear aeroelastic equations for combined flap-wise bending, chordwise bending, torsion and extension of twisted non-uniform rotor blades in forward flight," NASA TM-74059.
12. Mcguire, D. P., 1960, "The application of elastomeric lead-lag dampers to helicopter rotors," Lord Library No. LL2133.
13. Minguet, P. and Dugundji, J., 1990, "Experiments and analysis for composite blades under large deflection: Part 2. Dynamic behavior," AIAA Journal 28, 1580-1588.
14. Nayfeh, A. H., 1981, Introduction to Perturbation Technique, Wiley, New York.
15. Nayfeh, A. H. and Nayfeh, S. A., 1994, "Non-linear normal modes of a continuous system with quadratic non-linearities," Journal of Vibration and Acoustics 117, 199-205.
16. Nayfeh, A. H., Mook, D. T., and Lobitz, D. W., 1974, "Numerical-perturbation method for the non-linear analysis of structural vibrations," AIAA Journal 12, 1222-1228.
17. Nayfeh, A. H., Chin, C., and Nayfeh, S. A., 1995, "Non-linear normal modes of a cantilever beam," Journal of Vibration and Acoustics 117, 477-481.
18. Pakdemirli, M., and Nayfeh, A. H., 1994, "Non-linear vibration of a beam-spring-mass system," Journal of Vibration and Acoustics 116, 433-439.
19. Pesheck, E., Pierre, C., and Shaw, S. W., 2002, "Modal reduction of a non-linear rotating beam through normal modes," Journal of Vibration and Acoustics 124, 229-236.
20. Pohit, G., Mallik, A. K., and Venkatesan, C., 1999, "Free out-of-plane vibration of a rotating beam with non-linear elastomeric constraints," Journal of Sound and Vibration 220(1), 1-25.
21. Pohit, G., Venkatesan, C., and Mallik, A. K., 2000, "Elastomeric damper model and limit cycle oscillation in bearingless helicopter rotor blade," Journal of Aircraft 37(5), 923-926.
22. Pohit, G., Venkatesan, C., and Mallik, A. K., 2004, "Influence of non-linear elastomer on isolated lag dynamics and rotor/fuselage aeromechanical stability," Journal of Aircraft 41(6), 1449-1464.
23. Potter, J. L., 1959, "Improving reliability and eliminating maintenance with elastomeric dampers for rotor systems," Lord Library No. LL2120.
24. Rosen, A. and Friedmann, P. P., 1979, "The non-linear behavior of elastic slender straight beams undergoing small strains and moderate relations," Journal of Applied Mechanics 46, 161-168.
25. Smith, E. C., Beale, M. R., Govindswamy, K., Vascsineci, H. J., and Lesientre, G. A., 1995, "Formulation and validation of a finite element model for elastomeric lag dampers," in Proceedings of the 51st Annual Forum of the American Helicopter Society, Forth Worth, TX, May, pp. 1101-1116.