Modal analysis of a continuous gyroscopic second-order system with nonlinear constraints

Journal of Sound and Vibration

Volumn 329, Issue 7, 2010, Pages 893-911

  Brake, M R ^a   Wickert, J A ^b  

^a SANDIA NATIONAL LABORATORIES   (United States)

^b Iowa State University   (United States)

Author keywords

[No Author keywords available]

Indexed keywords

ARBITRARY POSITIONS; CHAOTIC BEHAVIORS; CONTACT STATE; DATA STORAGE SYSTEMS; DEFLECTION PROFILES; DESIGN PARAMETERS; FORCE DEFLECTION; GYROSCOPIC SYSTEM; INNER PRODUCT; MAPPING METHOD; MODE SHAPES; NON-LINEAR CONSTRAINTS; PERIODIC MOTION; PIECEWISE-LINEAR; SECOND-ORDER SYSTEMSS; STATIONARY SYSTEMS; TRANSPORT SPEED;

BIFURCATION (MATHEMATICS); FLANGES; MAGNETIC STORAGE; MAGNETIC TAPE; MAGNETIC TAPE STORAGE; MODAL ANALYSIS; PIECEWISE LINEAR TECHNIQUES; STIFFNESS; STRUCTURAL PANELS;

CHAOTIC SYSTEMS;

EID: 71249149235     PISSN: 0022460X     EISSN: 10958568     Source Type: Journal    
DOI: 10.1016/j.jsv.2009.10.004     Document Type: Article

References (38)

1. Zuo L., and Curnier A. Non-linear real and complex modes of conewise linear systems. Journal of Sound and Vibration 174 (1994) 289-313
2. Païdoussis M.P., and Semler C. Nonlinear and chaotic oscillations of a constrained cantilevered pipe conveying fluid: a full nonlinear analysis. Nonlinear Dynamics 4 (1993) 655-670
3. Zhu W.D., and Mote Jr. C.D. Propagation of boundary disturbances in an axially moving strip in contact with rigid and flexible constraints. ASME Journal of Applied Mechanics 62 (1995) 873-879
4. van Horssen W.T., and Ponomareva S.V. On the construction of an equation describing an axially moving string. Journal of Sound and Vibration 287 (2005) 359-366
5. Wickert J.A., and Mote Jr. C.D. Classical vibration analysis of axially moving continua. ASME Journal of Applied Mechanics 57 (1990) 738-744
6. Perkins N.C. Linear dynamics of a translating string on an elastic foundation. ASME Journal of Vibration and Acoustics 112 (1990) 2-7
7. Cheng S.-P., and Perkins N.C. The vibration and stability of a friction-guided, translating string. Journal of Sound and Vibration 144 (1991) 281-292
8. Chakraborty G., and Mallik A.K. Non-linear vibration of a travelling beam having an intermediate guide. Nonlinear Dynamics 20 (1999) 247-265
9. Jiang D., Pierre C., and Shaw S.W. Large-amplitude non-linear normal modes of piecewise linear systems. Journal of Sound and Vibration 272 (2004) 869-891
10. Luo A.C.J. The mapping dynamics of periodic motions for a three-piecewise linear system under a periodic excitation. Journal of Sound and Vibration 283 (2005) 723-748
11. Kerschen G., Worden K., Vakakis A.F., and Golinval J.-C. Past, present and future of nonlinear system identification in structural dynamics. Mechanical Systems and Signal Processing 20 (2006) 505-592
12. Ervin E.K., and Wickert J.A. Repetitive impact response of a beam structure subjected to harmonic base excitation. Journal of Sound and Vibration 307 (2007) 2-19
13. Metallidis P., and Natsiavas S. Vibration of a continuous system with clearance and motion constraints. International Journal of Non-Linear Mechanics 35 (2000) 675-690
14. Deshpande S., Mehta S., and Jazar G.N. Optimization of secondary suspension of piecewise linear vibration isolation systems. International Journal of Mechanical Sciences 48 (2006) 341-377
15. Luo G.W. Dynamics of an impact-forming machine. International Journal of Mechanical Sciences 48 (2006) 1295-1313
16. Fredriksson M.H., Borglund D., and Nordmark A.B. Experiments on the onset of impacting motion using a pipe conveying fluid. Nonlinear Dynamics 19 (1999) 261-271
17. Qiao N., Lin W., and Qin Q. Bifurcations and chaotic motions of a curved pipe conveying fluid with nonlinear constraints. Computers and Structures 84 (2006) 708-717
18. Lin W., Qiao N., and Yuying H. Dynamical behaviors of a fluid-conveying curved pipe subjected to motion constraints and harmonic excitations. Journal of Sound and Vibration 306 (2007) 955-967
19. Wickert J.A., and Mote Jr. C.D. Current research on the vibration and stability of axially-moving materials. Shock and Vibration Digest 20 (1988) 3-13
20. Young G.E., and Reid K.N. Lateral and longitudinal dynamic behavior and control of moving webs. ASME Journal of Dynamic Systems, Measurement, and Control 115 (1993) 309-317
21. Yerashunas J.B., Abreu-Garcia J.A.D., and Hartley T.T. Control of lateral motion in moving webs. IEEE Transactions on Control Systems Technology 11 (2003) 684-693
22. Chen L.-Q. Analysis and control of transverse vibrations of axially moving strings. ASME Applied Mechanics Reviews 58 (2005) 91-116
23. Brake M.R., and Wickert J.A. Frictional vibration transmission from a laterally moving surface to a traveling beam. Journal of Sound and Vibration 310 (2008) 663-675
24. Meirovitch L., and Ryland I.G. Response of slightly damped gyroscopic systems. Journal of Sound and Vibration 67 (1979) 1-19
25. Kartik V., and Wickert J.A. Vibration and guiding of moving media with edge weave imperfections. Journal of Sound and Vibration 291 (2006) 419-436
26. Azrar L., Boutyour E.H., and Potier-Ferry M. Non-linear forced vibrations of plates by an asymptotic-numerical method. Journal of Sound and Vibration 252 (2002) 657-674
27. Begley C.J., and Virgin L.N. Impact response and the influence of friction. Journal of Sound and Vibration 211 (1998) 801-818
28. Wagg D.J., and Bishop S.R. Application of non-smooth modeling techniques to the dynamics of a flexible impacting beam. Journal of Sound and Vibration 256 (2002) 803-820
29. Fegelman K.J.L., and Grosh K. Dynamics of a flexible beam contacting a linear spring at low frequency excitation: experiment and analysis. ASME Journal of Vibration and Acoustics 124 (2004) 237-249
30. Païdoussis M.P., and Li G.X. Cross-flow-induced chaotic vibrations of heat-exchanger tubes impacting on loose supports. Journal of Sound and Vibration 152 (1992) 305-326
31. Stefanski A. Estimation of the largest Lyapunov exponent in systems with impacts. Chaos, Solitons and Fractals 11 (2000) 2443-2451
32. de Souza S.L.T., and Caldas I.L. Calculation of Lyapunov exponents in systems with impacts. Chaos, Solitons and Fractals 19 (2004) 569-579
33. Shadden S.C., Lekien F., and Marsden J.E. Definition and properties of Lagrangian coherent structures from finite-time Lyapunov exponents in two-dimensional aperiodic flows. Physica D 212 (2005) 271-304
34. van de Vorst E.L.B., van Campen D.H., and de Kraker A. Periodic solutions of a multi-dof beam system with impact. Journal of Sound and Vibration 192 (1996) 913-925
35. Murphy K.D., and Morrison T.M. Grazing instabilities and post-bifurcation behavior in an impacting string. Journal of the Acoustical Society of America 111 (2002) 884-892
36. Hu H.Y. Primary resonance of a harmonically forced oscillator with a pair of symmetric set-up elastic stops. Journal of Sound and Vibration 207 (1997) 393-401
37. Maccari A. The response of a forced oscillator under the effect of a pair of set-up elastic stops. Journal of Sound and Vibration 235 (2000) 879-887
38. D. Mee (Ed.), International Magnetic Tape Storage Roadmap, Information Storage Industry Consortium, 2005.