Concise equations for improvements in computational efficiency on dynamics of rotor systems are presented. Two coordinate ordering methods are introduced in the element equations of motion. One is in the real domain and the other is in the complex domain. The two coordinate ordering algorithms lead to compact element matrices. A station numbering technique is also proposed for the system equations during the assembly process. The proposed numbering technique can minimize the matrix bandwidth, the memory storage and can increase the computational efficiency. Numerical examples are presented to demonstrate the benefit of the proposed algorithms.

Issue Section:
Research Papers
Topics:
Algorithms, Dynamics (Mechanics), Equations of motion, Manufacturing, Rotordynamics, Rotors, Storage
1.
Childs
D. W.
, and
Graviss
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,
1982
, “
A Note on Critical-Speed Solutions for Finite-Element-Based Rotor Models
,”
ASME Journal of Mechanical Design
, Vol.
104
, pp.
412
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416
.
2.
Chen, W. J., Zeidan, F. Y., and Jain, D., 1994, “Design, Analysis, and Testing of High Performance Bearings in a High Speed Integrally Geared Compressor,” Proceedings of 23rd Turbomachinery Symposium, Texas A&M University, Texas.
3.
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4.
Genta
G.
,
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, “
Whirling of Unsymmetrical Rotors: A Finite Element Approach based on Complex Co-ordinates
,”
Journal of Sound and Vibration
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124
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1
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27
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53
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5.
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6.
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7.
Nelson
H. D.
, and
Chen
W. J.
,
1993
, “
Undamped Critical Speeds of Rotor Systems Using Assumed Modes
,”
ASME JOURNAL OF VIBRATION AND ACOUSTICS
, Vol.
115
, pp.
367
–
369
.
8.
Nelson
H. D.
,
1985
, “
Rotor Dynamics Equations in Complex Form
,”
ASME JOURNAL OF VIBRATION, ACOUSTICS, STRESS, AND RELIABILITY IN DESIGN
, Vol.
107
, pp.
460
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461
.
9.
Nelson
H. D.
,
1980
, “
A Finite Rotating Shaft Element Using Timoshenko Beam Theory
,”
ASME Journal of Mechanical Design
, Vol.
102
, pp.
793
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802
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10.
Rouch
K. E.
, and
Kao
J. S.
,
1979
, “
A Tapered Beam Finite Element for Rotor Dynamics Analysis
,”
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11.
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12.
Shiau
T. N.
, and
Hwang
J. L.
,
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, “
A New Approach to the Dynamic Characteristic of Undamped Rotor-Bearing Systems
,”
ASME JOURNAL OF VIBRATION, ACOUSTICS, STRESS, AND RELIABILITY IN DESIGN
, Vol.
111
, pp.
379
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385
.
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