This study develops a numerical method for analyzing the unbalanced effect of rotary systems by combining the finite element method, the transfer matrix method, the time marching numerical integration method and the Houbolt numerical method. Previous studies of the individual effects associated with the rotary inertia, gyroscopic phenomenon, shear deformation, axial loading and internal damping on the dynamic behavior of rotary systems are all incorporated and examined in this study. The calculated transient and steady displacements of components in two systems are comparable with the available data. The results show that maximum displacements occur in the transient states at some critical speeds to assure the importance for analyzing the unbalanced effect of the rotary systems. Compared with existing methods, this presently combined methodology provides a faster converging speed. In addition, this model should improve the predicted results for the transient dynamic analysis of rotary systems than those obtained from existing models.

Issue Section:
Technical Papers
Keywords:
shear deformation, integration, damping, rotation, vibrations, finite element analysis, numerical analysis
Topics:
Damping, Disks, Displacement, Numerical analysis, Shear deformation, Transients (Dynamics), Bearings, Vibration
1.
Adams
,
M.
,
1980
, “
Nonlinear Dynamics of Multibearing Flexible Rotors
,”
J. Sound Vib.
,
71
, No.
1
, pp.
129
–
144
.
2.
Nelson
,
H. D.
,
1980
, “
A Finite Rotating Shaft Element Using Timoshenko Beam Theory
,”
ASME J. Mech. Des.
,
102
, pp.
793
–
803
.
3.
Dokainish
,
M. A.
,
1972
, “
A New Approach for Plate Vibrations: Combination of Transfer Matrix and Finite-Element Technique
,”
ASME J. Eng. Ind.
,
94
, pp.
526
–
530
.
4.
Pestel, E. C., and Leckie, F. A., 1963, Matrix Methods in Elastomechanics, McGraw-Hill, New York.
5.
Kumar
,
A. S.
, and
Sankar
,
T. S.
,
1986
, “
A New Transfer Matrix Method for Response Analysis of Large Dynamic Systems
,”
Comput. Struct.
,
23
, No.
4
, pp.
545
–
552
.
6.
Subbiah
,
R.
,
Sankar
,
T. S.
, and
Kumar
,
A. S.
,
1988
, “
Transient Dynamic Analysis of Rotors Using the Combined Methodologies of Finite Elements and Transfer Matrix
,”
ASME J. Appl. Mech.
,
55
, pp.
448
–
452
.
7.
Nelson
,
H. D.
, and
McVaugh
,
J. M.
,
1976
, “
The Dynamics of Rotor Bearing Systems Using Finite Elements
,”
ASME J. Eng. Ind.
, May, pp.
593
–
600
.
8.
Houbolt
,
J. C.
,
1950
, “
A Recurrence Matrix Solution for the Dynamic Response of Elastic Aircraft
,”
J. Aeronaut. Sci.
,
17
, pp.
540
–
550
.
9.
O¨zguven
,
N. H.
, and
O¨zkan
,
L. N.
,
1984
, “
Whirl Speeds and Unbalance Response of Multi-bearing Rotors Using Finite Elements
,”
ASME J. Vib. Acoust. Stress Reliab. Des.
,
106
, pp.
72
–
79
.
10.
Subbiah
,
R.
, and
Rieger
,
N. F.
,
1988
, “
On the Transient Analysis of Rotary Bearing Systems
,”
ASME J. Vib. Acoust. Stress, Reliab. Des.
,
110
, pp.
515
–
520
.
11.
Alam
,
M.
, and
Nelson
,
H. D.
,
1985
, “
A Blade Loss Response Spectrum for Flexible Rotor Systems
,”
ASME J. Eng. Gas Turbines Power
,
107
, pp.
187
–
204
.
12.
Newmark
,
M. N.
,
1959
, “
A Method of Computation for Structural Dynamics
,”
ASME J. Eng. Mech. Div.
,
85
, pp.
67
–
94
.
13.
Wilson
,
E. L.
,
Farhoomand
,
I.
, and
Bathe
,
K. J.
,
1973
, “
Nonlinear Dynamic Analysis of Complex Structures
,”
International Journ. of Earthquake Engineering And Structural Dynamics
,
1
, pp.
241
–
252
.
14.
Bathe, K. J., and Wilson, E. L., 1976, Numerical Methods in Finite Element Analysis, Prentice Hall, Englewood Cliffs, New Jersey.
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