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TECHNICAL PAPERS

Thermally Induced Vibration of an Internally Heated Beam

[+] Author and Article Information
Joseph R. Blandino

James Madison University, Harrisonburg, VA 22807

Earl A. Thornton

University of Virginia Charlottesville, VA 22901

J. Vib. Acoust 123(1), 67-75 (Jul 01, 2000) (9 pages) doi:10.1115/1.1320446 History: Received February 01, 2000; Revised July 01, 2000
Copyright © 2001 by ASME
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References

Boley,  B.A., 1956, “Thermally Induced Vibrations of Beams,” J. Aeronaut. Sci., 23, pp. 179–181.
Thornton, E.A., 1996, Thermal Structures for Aerospace Applications, AIAA Education Series, American Institute of Aeronautics and Astronautics, Inc., Washington, D.C.
Foster, R.S., 1998, “Thermally Induced Vibrations of Spacecraft Booms,” Doctoral dissertation, University of Virginia, Charlottesville, VA.
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.
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.
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.
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.
Johnston,  J.D., and Thornton,  E.A., 1996, “Thermal Response of Radiantly Heated Spinning Spacecraft Booms,” J. Thermophys. Heat Transfer, 10, pp. 60–68.
Johnston, J.D., 1995, “Thermal Response of Radiantly Heated Spinning Spacecraft Booms,” Master’s thesis, University of Virginia, Charlottesville, VA.
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.
Johnston, J.D., 1999, “Thermally-Induced Structural Motions of Satellite Solar Arrays,” Doctoral dissertation, University of Virginia, Charlottesville, VA.
Beam, R.M., 1969, “On the Phenomenon of Thermoelastic Instability (Thermal Flutter) of Booms with Open Cross Section,” NASA TN D-5222.
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.
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.
Baker,  J.G., 1933, “Self Induced Vibrations,” Trans. ASME, 55, pp 5–13.
Murozono, M., 1995, “Thermally Induced Bending Vibrations of Internally Heated Beams in Air,” unpublished Manuscript, Kyushu University.
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.
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).
Boley, B.A., and Weiner, J.H., 1985, Theory of Thermal Stresses, Robert E. Krieger Publishing, Malabar, FL, pp. 339–345.
Young, W.C., 1994, Roark’s Formulas for Stress and Strain, Sixth Edition, McGraw-Hill, New York, NY, pp. 714–715.
Kelly, S.G., Fundamentals of Mechanical Vibrations, McGraw-Hill, New York, NY, 1993, pp. 118–125.
Den Hartog, J.P., 1985, Mechanical Vibrations, Dover Publications, New York, NY, pp. 283–334.
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.

Figures

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Free body diagram of the deflected beam
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Cross section of tube with differential area dA and moment arm y
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Beam divided into ten equal sections for structural analysis
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Photograph of micrometer stage and electromagnet used to apply an initial displacement to the beam
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Isothermal free vibration displacement histories for two beams. (a) 0.98 Hz beam. (b) 1.37 Hz beam.
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Tip displacement and temperature histories for a beam with a natural frequency of 0.98 Hz heated with 12.6 W. (a) Tip displacement envelopes. (b) Temperature histories at X=783 mm.
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Displacement and temperature histories for a beam with a natural frequency of 0.98 Hz, heated with 28.4 W. (a) Tip displacement envelopes. (b) Temperature histories at X=783 mm.
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Tip displacement and temperature histories for a beam with a natural frequency of 1.37 Hz heated with 28.4 W. (a) Tip displacement envelopes. (b) Temperature histories at X=783 mm.
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Predicted time variation in the thermal moment and velocity at X=783 mm for a beam with a natural frequency for 0.98 Hz heated with 28.4 W. (a) Variation in the thermal moment with time. (b) Velocity variation with time.
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Predicted dependence of the steady-state vibration amplitude on frequency and heating rate
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Predicted behavior of a beam given two different initial displacements and heated with 12.6 W. (a) 50 mm initial displacement. (b) 7 mm initial displacement.

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