Coupled thermally induced vibrations of beams.

6 Orth, R. C. and Funk, J. A., An Experimental and Comparative Study of Jet Penetration in Supersonic Flow, Journal of Spacecraft and Rockets, Vol. 4, No. 9, Sept. 1967, pp. 1236-1242. 7 Billig, F. S., Orth, R. C., and Lasky, M, Unified Analysis of Gaseous Jet Penetration, AIAA Journal, Vol. 9, No. 6, June 1971, pp. 1048-1058. 8 Mullen, J. H., Madson, J. M., and Medgyesi-Mitschang, L. N., Ion Intensity Measurement in a Plasma Reaction Channel, AIAA Paper 72-675, Boston, Mass., 1972. reference absolute temperature T for the state of zero stress and strain, Iyy is the cross-sectional moment of inertia, A is the crosssectional area, p is the density, Kx is the Timoshenko shear coefficient, t is time, u is the transverse deformation, h is the beam depth, q the input heat flux, s is the circumferential arc length along the beam section, x and y are rectangular coordinates in the transverse beam directions, z is the rectangular coordinate in the beam lengthwise direction, and