Thermally Induced Bending Vibration of Thin-Walled Boom Caused by Radiant Heating

Abstract

The present report describes a theoretical analysis of the thermally induced bending vibration of the thin-walled boom with tip mass subjected to solar radiant heating. The governing equation and the time-dependent boundary conditions are formulated assuming that the boom is heated by the unidirectional solar radiation and that net absorption depends on the angle of incidence of heat radiation with respect to the boom. The methods of solution consist of applying the Laplace transform with respect to time to the equation and to the boundary conditions, and of obtaining the response by a numerical inversion of the transformed solution. Stability of the system is studied using the root locus, and the unstable boundary curves, which divide the parameter plane into regions of stability and instability according to the direction of radiation and four system parameters, are also studied.