In this paper, a model for the deformation of a rotating prismatic rod-like body is developed and analyzed. The novel feature of the model is its incorporation of the Poisson effect. As a result, it provides realistic solutions for the deformed states of steadily rotating rods. The model presented in this paper is also simplified to a nonlinear version of a classical model for rotating rods. Numerical continuation is used to solve the boundary value problems associated with these models.
Issue Section:
Technical Papers
1.
Antman, S. S., 1995, Nonlinear Problems of Elasticity, Springer-Verlag, New York.
2.
Leissa
, A.
, 1981
, “Vibrational Aspects of Rotating Turbomachinery Blades
,” Appl. Mech. Rev.
, 34
, pp. 629
–635
.3.
Rao
, J. S.
, 1987
, “Turbomachinery Blade Vibrations
,” Shock Vib. Dig.
, 19
, pp. 3
–10
.4.
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
.5.
Bhuta
, P.-G.
, and Jones
, J. P.
, 1963
, “On Axial Vibrations of a Whirling Bar
,” J. Acoust. Soc. Am.
, 35
, pp. 217
–221
.6.
Brunelle
, E. J.
, 1971
, “Stress Redistribution and Instability of Rotating Beams and Disks
,” AIAA J.
, 9
, pp. 758
–759
.7.
Hodges
, D. H.
, and Bless
, R. R.
, 1994
, “Axial Instability of Rotating Rods Revisited
,” Int. J. Non-Linear Mech.
, 29
, pp. 879
–887
.8.
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.
9.
Green
, A. E.
, and Laws
, N.
, 1966
, “A General Theory of Rods
,” Proc. R. Soc. London, Ser. A
, A293
, pp. 145
–155
.10.
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.
11.
Green
, A. E.
, and Naghdi
, P. M.
, 1979
, “On Thermal Effects in the Theory of Rods
,” Int. J. Solids Struct.
, 15
, pp. 829
–853
.12.
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
.1.
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
; 2.
1997
34
, 3211
–3212
.1.
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
.2.
O’Reilly, O. M., 2001, “On Coupled Longitudinal and Lateral Vibrations of Elastic Rods,” J. Sound Vib., to appear.
3.
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.
4.
Doedel
, E. J.
, 1997
, “Nonlinear Numerics
,” J. Franklin Inst.
, 334B
, pp. 1049
–1073
.5.
Seydel, R., 1988, From Equilibrium to Chaos: Practical Bifurcation and Stability Analysis, Elsevier, New York.
6.
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
.7.
O’Reilly
, O. M.
, 1998
, “On Constitutive Relations for Elastic Rods
,” Int. J. Solids Struct.
, 35
, pp. 1009
–1024
.8.
Antman
, S. S.
, and Carbone
, E. R.
, 1977
, “Shear and Necking Instabilities in Nonlinear Elasticity
,” J. Elast.
, 7
, pp. 125
–151
.9.
O’Reilly
, O. M.
, and Turcotte
, J. S.
, 1997
, “Elastic Rods With Moderate Rotation
,” J. Elast.
, 48
, pp. 193
–216
.10.
Berdichevskii
, V. L.
, 1981
, “On the energy of an elastic rod
,” J. Appl. Math. Mech.
, 45
, 518
–529
.11.
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
S211–S220
.12.
Chree
, C.
, 1889
, “On Longitudinal Vibrations
,” Quart. J. Pure Appl. Math.
, 23
, 317
–342
.13.
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.
14.
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
.15.
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
.Copyright © 2001
by ASME
You do not currently have access to this content.
