In this paper, the differential transformation approach is applied to analyze the free vibration of centrifugally stiffened Timoshenko beam structures. Such structures involve variable coefficients in the governing equations, which in general cannot be solved analytically in closed form. Both the natural frequencies and the mode shapes are obtained using the differential transformation technique. Numerical examples are presented and results are compared with available results in the literature.

1.
Hodges
,
D. H.
, and
Rutkowski
,
M. J.
, 1981, “
Free Vibation Analysis of Rotating Beams by a Variable Order Finite Element Method
,”
AIAA J.
0001-1452,
19
, pp.
1459
1466
.
2.
Wright
,
A. D.
,
Smith
,
C. E.
,
Thresher
,
R. W.
, and
Wang
,
J. L. C.
, 1982, “
Vibration Modes of Centrifugally Stiffened Beam
,”
Trans. ASME, J. Appl. Mech.
0021-8936,
49
, pp.
197
202
.
3.
Udupa
,
K. M.
, and
Varadan
,
T. K.
, 1990, “
Hierarchical Finite Element Method for Rotating Beams
,”
J. Sound Vib.
0022-460X,
138
, pp.
447
456
.
4.
Naguleswaran
,
S.
, 1994, “
Lateral Vibration of a Centrifugally Tensioned Uniform Euler-Bernoulli Beam
,”
J. Sound Vib.
0022-460X,
176
(
5
), pp.
613
624
.
5.
Banerjee
,
J. R.
, 2000, “
Free Vibration of Centrifugally Stiffened Uniform and Tapered Beams Using the Dynamic Stiffness Method
,”
J. Sound Vib.
0022-460X,
233
(
5
), pp.
857
875
.
6.
Rayleigh
,
L.
, 1926,
Theory of Sound
,
The Macmillan Company
, New York.
7.
Timoshenko
,
S. P.
, 1921, “
On the Correction for Shear of the Differential Equation for Transverse Vibrations of Prismatic Bars
,”
Philos. Mag.
0031-8086,
41
, pp.
744
746
.
8.
Timoshenko
,
S. P.
, 1922, “
On the Transverse Vibrations of Bars of Uniform Cross Sections
,”
Philos. Mag.
0031-8086,
43
, pp.
125
131
.
9.
Du
,
H.
,
Lim
,
M. K.
, and
Liew
,
K. M.
, 1994, “
A Power Series Solution for Vibration of a Rotating Timoshenko Beam
,”
J. Sound Vib.
0022-460X,
175
(
4
), pp.
505
523
.
10.
Bazoune
,
A.
,
Khulief
,
Y. A.
, and
Stephen
,
N. G.
, 1999, “
Further Results for Modal Characteristics of Rotating Tapered Timoshenko Beams
,”
J. Sound Vib.
0022-460X,
219
, pp.
157
174
.
11.
Banerjee
,
J. R.
, 2001, “
Dynamic Stiffness Formulation and Free Vibration Analysis of Centrifugally Stiffened Timoshenko Beams
,”
J. Sound Vib.
0022-460X,
247
(
1
), pp.
97
115
.
12.
Pnueli
,
D.
, 1972, “
Natural Bending Frequency Comparable to Rotational Frequency in Rotating Cantilever Beam
,”
Trans. ASME, J. Appl. Mech.
0021-8936,
39
, pp.
602
604
.
13.
Fox
,
C. H. J.
, and
Burdess
,
J. S.
, 1979, “
The Natural Frequencies of a Thin Rotating Cantilever With Offset Root
,”
J. Sound Vib.
0022-460X,
65
, pp.
151
158
.
14.
Zhou
,
J. K.
, 1986,
Differential Transformation and its Applications for Electrical Circuits
,
Huazhong University Press
, Wuhan, China.
15.
Chen
,
C. K.
, and
Ho
,
S. H.
, 1996, “
Application of Differential Transformation to Eigenvalue Problem
,”
Appl. Math. Comput.
0096-3003,
79
, pp.
504
510
.
16.
Chen
,
C. K.
, and
Ho
,
S. H.
, 1999, “
Transverse Vibration of a Rotating Twisted Timoshenko Beam Under Axia Loading Using Differential Transformation
,”
Int. J. Mech. Sci.
0020-7403,
41
, pp.
1339
1356
.
17.
Malik
,
M.
, and
Dang
,
H. H.
, 1998, “
Vibration Analysis of Continuous Systems by Differential Trans-Forrnation
,”
J. Appl. Math. Comput.
,
96
, pp.
17
26
.
18.
Zeng
,
H.
, and
Bert
,
C. W.
, 2001, “
Vibration Analysis of a Tapered Bar by Differential Transformation
,”
J. Sound Vib.
0022-460X,
242
(
4
), pp.
737
739
.
19.
Bert
,
C. W.
, and
Zeng
,
H.
, 2004, “
Analysis of Axial Vibration of Compound Bars by Differential Transformation Method
,”
J. Sound Vib.
0022-460X,
275
, pp.
641
647
.
20.
Jang
,
M. J.
, and
Chen
,
C. L.
, 1997, “
Analysis of the Response of a Strongly Nonlinear Damped System Using a Differential Transformation Technique
,”
Appl. Math. Comput.
0096-3003,
88
, pp.
137
151
.
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