A new exact approach for the analysis of torsional vibration of a non-uniform shaft carrying an arbitrary number of rigid disks is presented. The exact solutions for non-uniform shafts with arbitrary distribution of torsional stiffness or mass polar moment of inertia are obtained for several important cases. The fundamental solutions developed in this paper lead to a single frequency equation for a non-uniform shaft with classical or non-classical boundary conditions and carrying an arbitrary number of rigid disks.
Issue Section:
Technical Briefs
Keywords:
vibrations
1.
Housner. G. W., and Vreeland, T., 1967, Analytical Methods in Vibrations, Macmillan Publishing Co., New York.
2.
Richard
, J.
, 1972
, “Vibration De Torsion D’arbre De Section Variable
,” Reoue Francaise de Me’canique
,44
, pp. 13
–20
.3.
Eisenberger
, M.
, 1991
, “Exact Longitudinal Vibration Frequencies of a Variable Cross-Section Rod
,” Appl. Acoust.
, 34
, pp. 123
–130
.4.
Li
, Q. S.
, Li
, G. Q.
, and Liu
, D. K.
, 2000
, “Exact Solutions for Longitudinal Vibration of Rods Coupled by Translational Springs
,” Int. J. Mech. Sci.
, 42
, pp. 1135
–1152
.5.
Pouyet
, J. M.
, and Latailads
, J. L.
, 1981
, “Torsional Vibrations of a Shaft with Non-Uniform Cross Section
,” J. Sound Vib.
, 76
(1
), pp. 13
–22
.6.
Fitzgeorge
, D.
, and Williams
, F. W.
, 1976
, “Compact Distributed Inertia Solution for Free Torsional Vibrations of Shaft and Rotor System
,” J. Sound Vib.
, 46
, pp. 311
–322
.7.
Bapat
, C. N.
, and Bhutani
, N.
, 1994
, “General Approach for Free and Forced Vibrations of Stepped Systems Governed by the One-Dimensional Wave Equation with Non-Classical Boundary Conditions
,” J. Sound Vib.
, 172
(1
), pp. 1
—22
.8.
Li
, Q. S.
, Cao
, H.
, and Li
, G. Q.
, 1996
, “Static and Dynamic Analysis of Straight Bars with Variable Cross-Section
,” Comput. Struct.
59
, pp. 1185
–1191
.Copyright © 2002
by ASME
You do not currently have access to this content.