0
TECHNICAL PAPERS

On the Steady Motions of a Rotating Elastic Rod

[+] Author and Article Information
N. M. Kinkaid, O. M. O’Reilly

Department of Mechanical Engineering, University of Berkeley, Berkeley, CA 94720-1740

J. S. Turcotte

AFRL/VAS, Building 45, 2130 Eighth Street, Suite 1, Wright-Patterson AFB, OH 45433-7765

J. Appl. Mech 68(5), 766-771 (Jan 02, 2001) (6 pages) doi:10.1115/1.1381003 History: Received August 16, 2000; Revised January 02, 2001
Copyright © 2001 by ASME
Your Session has timed out. Please sign back in to continue.

References

Antman, S. S., 1995, Nonlinear Problems of Elasticity, Springer-Verlag, New York.
Leissa,  A., 1981, “Vibrational Aspects of Rotating Turbomachinery Blades,” Appl. Mech. Rev., 34, pp. 629–635.
Rao,  J. S., 1987, “Turbomachinery Blade Vibrations,” Shock Vib. Dig., 19, pp. 3–10.
Wright,  A. D., Smith,  C. E., Thresher,  R. W., and Wang,  J. L. C., 1982, “Vibration Modes of Centrifugally Stiffened Beams,” ASME J. Appl. Mech., 49, pp. 197–202.
Bhuta,  P.-G., and Jones,  J. P., 1963, “On Axial Vibrations of a Whirling Bar,” J. Acoust. Soc. Am., 35, pp. 217–221.
Brunelle,  E. J., 1971, “Stress Redistribution and Instability of Rotating Beams and Disks,” AIAA J., 9, pp. 758–759.
Hodges,  D. H., and Bless,  R. R., 1994, “Axial Instability of Rotating Rods Revisited,” Int. J. Non-Linear Mech., 29, pp. 879–887.
O’Reilly, O. M., and Turcotte, J. S., 1997, “On the free vibration of a whirling rod,” Proceedings of DETC’97: 1997 ASME Design Engineering Technical Conferences, Paper Number DETC97VIB4072.
Green,  A. E., and Laws,  N., 1966, “A General Theory of Rods,” Proc. R. Soc. London, Ser. A, A293, pp. 145–155.
Naghdi, P. M., 1982, “Finite Deformation of Elastic Rods and Shells,” Proceedings of the IUTAM Symposium on Finite Elasticity, D. E. Carlson and R. T. Shield, eds., Martinus Nijhoff, The Hague, pp. 47–104.
Green,  A. E., and Naghdi,  P. M., 1979, “On Thermal Effects in the Theory of Rods,” Int. J. Solids Struct., 15, pp. 829–853.
Naghdi,  P. M., and Rubin,  M. B., 1989, “On the Significance of Normal Cross-Sectional Extension in Beam Theory With Application to Contact Problems,” Int. J. Solids Struct., 25, pp. 249–265.
Nordenholz,  T. R., and O’Reilly,  O. M., 1997, “On Steady Motions of an Elastic Rod With Application to Contact Problems,” Int. J. Solids Struct., 34, pp. 1123–1143; 199734, 3211–3212.
Krishnaswamy,  S., and Batra,  R. C., 1998, “On Extensional Vibration Modes of Elastic Rods of Finite Length Which Include the Effect of Lateral Deformation,” J. Sound Vib., 215, pp. 577–586.
O’Reilly, O. M., 2001, “On Coupled Longitudinal and Lateral Vibrations of Elastic Rods,” J. Sound Vib., to appear.
Doedel, E. J., Champneys, A. R., Fairgrieve, T. F., Kuznetsov, Y. A., Sandstede, B., and Wang, X., 1997, “AUTO97: Continuation and bifurcation software for ordinary differential equations (with HomCont),” Department of Computer Science, Concordia University, Montreal, Canada.
Doedel,  E. J., 1997, “Nonlinear Numerics,” J. Franklin Inst., 334B, pp. 1049–1073.
Seydel, R., 1988, From Equilibrium to Chaos: Practical Bifurcation and Stability Analysis, Elsevier, New York.
Green,  A. E., Laws,  N., and Naghdi,  P. M., 1967, “A Linear Theory of Straight Elastic Rods,” Arch. Ration. Mech. Anal., 25, pp. 285–298.
O’Reilly,  O. M., 1998, “On Constitutive Relations for Elastic Rods,” Int. J. Solids Struct., 35, pp. 1009–1024.
Antman,  S. S., and Carbone,  E. R., 1977, “Shear and Necking Instabilities in Nonlinear Elasticity,” J. Elast., 7, pp. 125–151.
O’Reilly,  O. M., and Turcotte,  J. S., 1997, “Elastic Rods With Moderate Rotation,” J. Elast., 48, pp. 193–216.
Berdichevskii,  V. L., 1981, “On the energy of an elastic rod,” J. Appl. Math. Mech., 45, 518–529.
Cesnik,  C. E. S., and Hodges,  D. H., 1993, “Variational-asymptotical analysis of initially curved and twisted composite beams,” Appl. Mech. Rev., 46(11/2), S211–S220.
Chree,  C., 1889, “On Longitudinal Vibrations,” Quart. J. Pure Appl. Math., 23, 317–342.
Cremer, L., Heckl, M., and Ungar E. E., 1988, Structure-Borne Sound: Structural Vibrations and Sound Radiation at Audio Frequencies, 2nd Ed., Springer-Verlag, New York.
Lakin,  D. A., and Nachman,  A., 1979, “Vibration and Buckling of Rotating Flexible Rods at Transitional Parameter Values,” J. Eng. Math., 13, pp. 339–346.
O’Reilly,  O. M., and Varadi,  P. C., 1999, “A Treatment of Shocks in One-Dimensional Thermomechanical Media,” Continuum Mech. Thermodyn., 11, pp. 339–352.

Figures

Grahic Jump Location
A rod-like body rotating with an angular speed Ω about the E1-axis. The angle θ of rotation is such that θ̇=Ω.
Grahic Jump Location
The reference configuration of the rod-like body
Grahic Jump Location
The dimensionless axial displacement u(s) and lateral strains γ11(s) and γ22(s) for various values of ω: (i), ω2=0.5; (ii), ω2=1.0; (iii), ω2=1.5; (iv), ω2=2.0, and (v), ω2=2.64. For these results, ν=0.3 and a rod whose length is ten times its height and width was considered: h/L=w/L=0.1.
Grahic Jump Location
The dimensionless lateral strain γ22(s) for various values of ω: (i), ω2=0.5; (ii), ω2=1.0; (iii), ω2=1.5; (iv), ω2=2.0, and (v), ω2=2.64. For these results, ν=0.3 and a rectangular cross section was considered: h/L=0.1 and w/L=0.05.
Grahic Jump Location
The dimensionless axial displacement u(s) predicted by the uniaxial model (18) for various values of ω: (i), ω2=0.5; (ii), ω2=1.0; (iii), ω2=2.5; (iv), ω2=5.0; (v) ω2=10.0; and (vi), ω2=15.0.
Grahic Jump Location
The dimensionless displacement Δu(s) for various values of ω: (i), ω2=0.5; (ii), ω2=1.0; (iii), ω2=1.5; (iv), ω2=2.0, and (v), ω2=2.64. For these results, ν=0.3 and a square cross section was considered: h/L=w/L=0.1.

Tables

Errata

Discussions

Some tools below are only available to our subscribers or users with an online account.

Related Content

Customize your page view by dragging and repositioning the boxes below.

Related Journal Articles
Related eBook Content
Topic Collections

Sorry! You do not have access to this content. For assistance or to subscribe, please contact us:

  • TELEPHONE: 1-800-843-2763 (Toll-free in the USA)
  • EMAIL: asmedigitalcollection@asme.org
Sign In