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.
Issue Section:
Technical Papers
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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