Virtually all previous research on thermally induced vibrations has investigated vibrations caused by surface heating. This paper describes the first detailed study of a thermally induced vibration caused by internal heating. A mathematical model was developed to predict the thermal-structural behavior of an internally heated beam. The results from the model were verified using experimental data for an internally heated beam undergoing thermally induced vibrations. The model was shown to predict the steady-state temperatures accurately. The model predicted the steady-state displacements adequately, although it predicted the displacement histories with some error. The analysis showed that the natural frequency of the beam was more important than the heating rate in determining if vibrations will occur. Once initiated, the amplitude of the vibration increased until the amplitude was such that the heat removed by convection balanced the internal heating. The steady-state amplitude was not affected by the initial displacement of the beam. The convection heat transfer caused the vibrations and controlled the steady-state amplitude. This study showed that thermally induced vibrations of internally heated beams belong to the class of vibrations called self-sustaining oscillations.

Issue Section:
Technical Papers
Keywords:
vibrations, heat conduction
Topics:
Displacement, Heating, Temperature, Vibration
1.
Boley
,
B.A.
,
1956
, “
Thermally Induced Vibrations of Beams
,”
J. Aeronaut. Sci.
,
23
, pp.
179
–
181
.
2.
Thornton, E.A., 1996, Thermal Structures for Aerospace Applications, AIAA Education Series, American Institute of Aeronautics and Astronautics, Inc., Washington, D.C.
3.
Foster, R.S., 1998, “Thermally Induced Vibrations of Spacecraft Booms,” Doctoral dissertation, University of Virginia, Charlottesville, VA.
4.
Thornton, E.A., and Foster, R.S., 1992, “Dynamic Response of Rapidly Heated Space Structures,” Computational Nonlinear Mechanics in Aerospace Engineering, S.N. Alturi, ed., Vol. 146, Progress in Astronautics and Aeronautics, AIAA, Washington, DC, pp. 451–477.
5.
Thornton
,
E.A.
, and
Kim
,
Y.A.
,
1993
, “
Thermally Induced Bending Vibrations of a Flexible Rolled-Up Solar Array
,”
J. Spacecr. Rockets
,
30
, pp.
438
–
448
.
6.
Murozono
,
M.
, and
Thornton
,
E.A.
,
1998
, “
Buckling and Quasistatic Thermal-Sructural Response of an Asymmetric Rolled-Up Solar Array
,”
J. Spacecr. Rockets
,
35
, pp.
147
–
155
.
7.
Thornton
,
E.A.
,
Chini
,
G.P.
, and
Gulick
,
D.W.
,
1995
, “
Thermally-Induced Vibrations of a Self-Shadowed Split Blanket Solar Array
,”
J. Spacecr. Rockets
,
32
, pp.
302
–
311
.
8.
Johnston
,
J.D.
, and
Thornton
,
E.A.
,
1996
, “
Thermal Response of Radiantly Heated Spinning Spacecraft Booms
,”
J. Thermophys. Heat Transfer
,
10
, pp.
60
–
68
.
9.
Johnston, J.D., 1995, “Thermal Response of Radiantly Heated Spinning Spacecraft Booms,” Master’s thesis, University of Virginia, Charlottesville, VA.
10.
Gulick
,
D.W.
, and
Thornton
,
E.A.
,
1995
, “
Thermally Induced Vibrations of an Axial Boom on a Spin-Stabilized Spacecraft
,”
Acta Astronaut.
,
36
, pp.
163
–
176
.
11.
Johnston, J.D., 1999, “Thermally-Induced Structural Motions of Satellite Solar Arrays,” Doctoral dissertation, University of Virginia, Charlottesville, VA.
12.
Beam, R.M., 1969, “On the Phenomenon of Thermoelastic Instability (Thermal Flutter) of Booms with Open Cross Section,” NASA TN D-5222.
13.
Rimrott
,
R.P.J.
, and
Abdel-Sayed
,
R.
,
1977
, “
Flexural Thermal Flutter Under Laboratory Conditions
,”
Transactions of the Canadian Society of Mechanical Engineers
,
4
, pp.
189
–
196
.
14.
Baker
,
J.G.
, and
Mikina
,
S.J.
,
1937
, “
The Calculation of Dampers for Systems Subject to Self-Induced Vibration
,”
ASME J. Appl. Mech.
,
59
, pp.
A121–A126
A121–A126
.
15.
Baker
,
J.G.
,
1933
, “
Self Induced Vibrations
,”
Trans. ASME
,
55
,
5
–
13
.
16.
Murozono, M., 1995, “Thermally Induced Bending Vibrations of Internally Heated Beams in Air,” unpublished Manuscript, Kyushu University.
17.
Blandino, J.R., and Thornton E.A., 2000, “Determination of Heat Transfer Coefficients from a Vertical Vibrating Beam,” AIAA-2000-2577, Proceedings of the AIAA 34th Thermophysics Conference, June 19-22, 2000, Denver, CO.
18.
Sumi
,
S.
,
Murozono
,
M.
, and
Imoto
,
T.
,
1988
, “
Thermally-Induced Bending Vibration of Thin-Walled Boom with Tip Mass Caused by Radiant Heating
,”
Technology Reports of Kyushu University
,
61
, Fukuoka, Japan, pp.
449
–
455
(in Japanese with English abstract).
19.
Boley, B.A., and Weiner, J.H., 1985, Theory of Thermal Stresses, Robert E. Krieger Publishing, Malabar, FL, pp. 339–345.
20.
Young, W.C., 1994, Roark’s Formulas for Stress and Strain, Sixth Edition, McGraw-Hill, New York, NY, pp. 714–715.
21.
Kelly, S.G., Fundamentals of Mechanical Vibrations, McGraw-Hill, New York, NY, 1993, pp. 118–125.
22.
Den Hartog, J.P., 1985, Mechanical Vibrations, Dover Publications, New York, NY, pp. 283–334.
23.
Nayfeh, A.H., and Mook, D.T., 1979, Nonlinear Oscillations, Pure and Applied Mathematics, A Wiley-Interscience Series of Texts, Monographs, and Tracts, Wiley, New York, NY, pp. 103–131.
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