Journal of Zhejiang University-SCIENCE A

, Volume 8, Issue 7, pp 1044–1052 | Cite as

Effect of boundary conditions and convection on thermally induced motion of beams subjected to internal heating

  • Malik Pravin 
  • Kadoli Ravikiran 
  • Ganesan N. 


Numerical exercises are presented on the thermally induced motion of internally heated beams under various heat transfer and structural boundary conditions. The dynamic displacement and dynamic thermal moment of the beam are analyzed taking into consideration that the temperature gradient is independent as well as dependent on the beam displacement. The effect of length to thickness ratio of the beam on the thermally induced vibration is also investigated. The type of boundary conditions has its influence on the magnitude of dynamic displacement and dynamic thermal moment. A sustained thermally induced motion is observed with progress of time when the temperature gradient being evaluated is dependent on the forced convection generated due to beam motion. A finite element method (FEM) is used to solve the structural equation of motion as well as the heat transfer equation.

Key words

Thermal induced oscillations Natural convection Forced convection Finite element analysis 

CLC number



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  1. Boley, B.A., 1956. Thermally induced vibrations of beams. Journal of Aeronautical Science, 23:179–181.MathSciNetMATHGoogle Scholar
  2. Boley, B.A., 1972. Approximate analysis of thermally induced vibrations of beams and plates. Journal of Applied Mechanics, 39:212–216.CrossRefGoogle Scholar
  3. Boley, B.A., Barber, A.D., 1957. Dynamic response of beams and plates to rapid heating. Journal of Applied Mechanics, 24:413–416.MathSciNetMATHGoogle Scholar
  4. Carslaw, H.S., Jaeger, J.C., 1959. Conduction of Heat in Solids (2nd Ed.). Clarendon Press, Oxford.MATHGoogle Scholar
  5. Gulick, D.W., Thornton, E.A., 1995. Thermally-induced vibrations of a spinning spacecraft boom. Acta Astronautica, 36(3):163–176. [doi:10.1016/0094-5765(95)00097-J]CrossRefGoogle Scholar
  6. Incropera, F.P., DeWitt, D.P., 2002. Fundamentals of Heat and Mass Transfer (5th Ed.). John Wiley and Sons (Asia) Pte. Ltd., Singapore, p.399–414.Google Scholar
  7. Johnston, J.D., Thornton, E.A., 2000. Thermally induced dynamics of satellite solar panels. Journal of Spacecraft and Rockets, 37(5):604–613.CrossRefGoogle Scholar
  8. Kidawa-Kukla, J., 1997. Vibration of a beam induced by harmonic motion of a heat source. Journal of Sound and Vibration, 205(2):213–222. [doi:10.1006/jsvi.1997.0980]CrossRefMATHGoogle Scholar
  9. Kidawa-Kukla, J., 2003. Application of the Green functions to the problem of the thermally induced vibration of a beam. Journal of Sound and Vibration, 262(4):865–876. [doi:10.1016/S0022-460X(02)01133-1]CrossRefMATHGoogle Scholar
  10. Lyons, W.C., 1966. Comments on heat induced vibrations of Elastic beams, plates and shells. AIAA Journal, 4:1502–1503.CrossRefGoogle Scholar
  11. Manolis, G.D., Beskos, D.E., 1980. Thermally induced vibrations of beam structures. Computer Methods in Applied Mechanics and Engineering, 21(3):337–355. [doi:10.1016/0045-7825(80)90101-2]MathSciNetCrossRefMATHGoogle Scholar
  12. Seibert, A.G., Rice, J.S., 1973. Coupled thermally induced vibrations of beams. AIAA Journal, 7(7):1033–1035.Google Scholar
  13. Stroud, R.C., Mayers, J., 1971. Dynamic response of rapidly heated plate elements. AIAA Journal, 9(1):76–83.CrossRefGoogle Scholar
  14. Thornton, E.A., Foster, R.S., 1992. Dynamic Response of Rapidly Heated Space Structures. In: Alturi, S.N. (Ed.), Computational Nonlinear Mechanics in Aerospace Engineering, Progress in Astronautics and Aeronautics, AIAA. Washington, DC, 146:451–477.Google Scholar
  15. Thornton, E.A., Kim, Y.A., 1993. Thermally induced bending vibrations of a flexible rolled-up solar array. Journal of Spacecraft and Rockets, 30:438–448.CrossRefGoogle Scholar

Copyright information

© Springer-Verlag 2007

Authors and Affiliations

  • Malik Pravin 
    • 1
  • Kadoli Ravikiran 
    • 1
  • Ganesan N. 
    • 2
  1. 1.Department of Mechanical EngineeringNational Institute of Technology KarnatakaSurathkal, SrinivasnagarIndia
  2. 2.Department of Mechanical EngineeringIndian Institute of Technology MadrasChennaiIndia

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