Abstract
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.
Similar content being viewed by others
References
Boley, B.A., 1956. Thermally induced vibrations of beams. Journal of Aeronautical Science, 23:179–181.
Boley, B.A., 1972. Approximate analysis of thermally induced vibrations of beams and plates. Journal of Applied Mechanics, 39:212–216.
Boley, B.A., Barber, A.D., 1957. Dynamic response of beams and plates to rapid heating. Journal of Applied Mechanics, 24:413–416.
Carslaw, H.S., Jaeger, J.C., 1959. Conduction of Heat in Solids (2nd Ed.). Clarendon Press, Oxford.
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]
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.
Johnston, J.D., Thornton, E.A., 2000. Thermally induced dynamics of satellite solar panels. Journal of Spacecraft and Rockets, 37(5):604–613.
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]
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]
Lyons, W.C., 1966. Comments on heat induced vibrations of Elastic beams, plates and shells. AIAA Journal, 4:1502–1503.
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]
Seibert, A.G., Rice, J.S., 1973. Coupled thermally induced vibrations of beams. AIAA Journal, 7(7):1033–1035.
Stroud, R.C., Mayers, J., 1971. Dynamic response of rapidly heated plate elements. AIAA Journal, 9(1):76–83.
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.
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.
Author information
Authors and Affiliations
Rights and permissions
About this article
Cite this article
Malik, P., Kadoli, R. & Ganesan, N. Effect of boundary conditions and convection on thermally induced motion of beams subjected to internal heating. J. Zhejiang Univ. - Sci. A 8, 1044–1052 (2007). https://doi.org/10.1631/jzus.2007.A1044
Received:
Accepted:
Published:
Issue Date:
DOI: https://doi.org/10.1631/jzus.2007.A1044