THERMALLY INDUCED VIBRATION AND FLUTTER OF A FLEXIBLE BOOM

Thermally induced vibrations of spacecraft booms are known to have taken place. An analytical study of such vibrations and their stability is presented here for the first time. On the basis of Hamilton's principle, the problem is formulated by taking the boom with a tip mass as a cantilever beam and considering the bending vibration without twisting. The thermal curvature is assumed to be linearly related to the local heat input and governed by a differential equation of the first order in time involving a characteristic time constant. Although the governing equations are more involved than the usual beam equations, natural modes of an ordinary cantilever still can be employed in a variational approximation that yields the response. Stability is first investigated on the basis of single modes and zero damping. It is found that motion is stable if the boom is pointed away from the sun and unstable if it is pointed towards the sun, and the tip mass does not have much effect on stability. Presence of more than one mode does not seem to alter these results. Damping is next incorporated. Internal viscoelastic damping of ordinary boom materials is found to have little effect on stability, but a viscous- fluid damper of the ball-in-sphere type added at the tip of a boom can be effective for preventing thermal flutter. Important design parameters for the damper are identified, and design criteria for stability are presented. © 1969 American Institute of Aeronautics and Astronautics, Inc., All rights reserved.