This study develops dynamic analysis based on the dynamic stiffness method for a rotating beam of nonuniform cross-section. To deal with nonuniform beams, coefficients related to material and geometric properties in the equation of motion are expressed in a polynomial form. A dynamic stiffness matrix is accordingly formulated in terms of power series. The dynamic response of the rotating beam is calculated by performing modal analysis. It is demonstrated that the present method provides an alternative to the finite element method in dealing with nonuniform rotating beams.

Issue Section:
Technical Briefs
Keywords:
modal analysis, dynamic response, vibrations, rotation
Topics:
Cross section (Physics), Dynamic analysis, Dynamic response, Modal analysis, Rotating beams, Stiffness, Vibration, Rotation
1.
Ankarali
,
A.
, and
Diken
,
H.
,
1997
, “
Vibration Control of an Elastic Manipulator Link
,”
J. Sound Vib.
,
204
, No.
1
, pp.
162
–
170
.
2.
Simo
,
J. C.
, and
Vu-Quoc
,
L.
,
1986
, “
On the Dynamics of Flexible Beams under Large Overall Motions-the Plane Case: Part I
,”
ASME J. Appl. Mech.
,
53
, No.
4
, pp.
849
–
854
.
3.
Mayo
,
J.
, and
Dominguez
,
J.
,
1997
, “
A Finite Element Geometrically Nonlinear Dynamic Formulation of Flexible Multibody Systems Using a New Displacements Representation
,”
ASME J. Vibr. Acoust.
,
119
, No.
4
, pp.
573
–
581
.
4.
Ashar, K. G., 1997, Magnetic Disk Drive Technology, IEEE Press, New York.
5.
Eisenberger
,
M.
,
1990
, “
Exact Static and Dynamic Stiffness Matrices for Variable Cross Section Members
,”
AIAA J.
,
28
, No.
6
, pp.
1105
–
1109
.
6.
Leung
,
A. Y. T.
, and
Zhou
,
W. E.
,
1995
, “
Dynamic Stiffness Analysis of Non-Uniform Timoshenko Beams
,”
J. Sound Vib.
,
181
, No.
3
, pp.
447
–
456
.
7.
Liu
,
T. S.
, and
Lin
,
J. C.
,
1993
, “
Forced Vibration of Flexible Body System: a Dynamic Stiffness Method
,”
ASME J. Vibr. Acoust.
,
115
, No.
4
, pp.
468
–
476
.
8.
Richards
,
T. H.
, and
Leung
,
A. Y. T.
,
1977
, “
An Accurate Method in Structural Vibrating Analysis
,”
J. Sound Vib.
,
55
, No.
3
, pp.
363
–
376
.
9.
Bakr
,
E. M.
, and
Shabana
,
A. A.
,
1986
, “
Geometrically Nonlinear Analysis of Multibody Systems
,”
Comput. Struct.
,
23
, No.
6
, pp.
739
–
751
.
Copyright © 2001
 by ASME
You do not currently have access to this content.