The problem of calculating the vibrations of rotating structures has challenged analysts since the observation that use of traditional modal coordinates in such problems leads to the prediction of instability involving infinite deformation when rotation rates exceed the first natural frequency. A method using a system of nonlinearly coupled deformation modes to analyze rotating general, linear (unjointed) structures that addresses the problem of erroneously predicting infinite deformations has been presented in a preceding paper (Segalman and Dohrmann, 1995). This technique is employed to address several types of problems ranging from simple beams to an inflated membrane structure. Some of the details of exploiting existing finite element codes to evaluate the relevant matrices are also developed.

1.
Blevins, R. D., 1979, Formulas for Natural Frequency and Mode Shape, Van Nostrand Reinhold Company, New York, pp. 108.
2.
Cook, R. D., 1981, Concepts and Applications of Finite Element Analysis, John Wiley and Sons, New York, pp. 331–340.
3.
Kane
T. R.
,
Ryan
R. R.
, and
Banerjee
A. K.
,
1987
, “
Dynamics of a Cantilever Beam Attached to a Moving Base
,”
AIAA J. Guidance, Control, and Dynamics
, Vol.
10
, pp.
139
151
.
4.
Segalman, D. J., and Dohrmann, C. R., 1990, “Dynamics of Rotating Flexible Structures by a Method of Quadratic Modes,” Sandia Report SAND90-2737, available through the National Technical Information Service, Springfield, VA.
5.
Segalman, D. J., and Slavin, A. M., 1993, “Predicting the Vibrations of a Spinning Inflated Membrane,” Proceedings of 14th Biennial Conference On Mechanical Vibration And Noise, Albuquerque, Sept. 20–22.
6.
Segalman, D. J., and Dohrmann, C. R., 1995, “A Method for Calculating the Dynamics of Rotating Flexible Structures, Part 1: Derivation,” ASME JOURNAL OF VIBRATION AND ACOUSTICS.
7.
Simo
J. C.
, and
Vu-Quoc
L.
,
1986
a, “
On the Dynamics of Flexible Beams under Large Overall Motions—The Plane Case: Part I
,”
ASME Journal of Applied Mechanics
, Vol.
53
, pp.
849
854
.
8.
Simo
J. C.
, and
Vu-Quoc
L.
,
1986
b, “
On the Dynamics of Flexible Beams under Large Overall Motions—The Plane Case: Part II
,”
ASME Journal of Applied Mechanics
, Vol.
53
, pp.
855
863
.
9.
Simo
J. C.
, and
Vu-Quoc
L.
,
1987
, “
The Role of Non-Linear Theories in Transient Dynamic Analysis of Flexible Structures
,”
Journal of Sound and Vibration
, Vol.
119
, pp.
487
508
.
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