Solar induced bending vibrations of a flexible member

The stability of in-plane bending oscillations of long flexible members (STEMs) when subjected to solar heating is examined. The model accounts for the interdependence between the time varying STEM thermal curvature (caused by its changing temperature distribution) and the STEM bending motion. The linearized response of the STEM is determined in the Laplace transformed time domain and the ensuing stability criterion is found to be dependent upon, along with other parameters, the sun orientation, the material surface absorptivity and the extent of damping in the STEM, the latter being due mainly to the friction in the overlapped or interlocked part of the STEM element. In the case where the STEM is oriented towards the sun the motion is shown to be stable. The use of the best available values of absorptivity and damping shows stability to be marginal for silver-plated STEM in the case where the STEM is oriented away from the sun. More accurate test information on the mechanism and magnitude of damping is required to accurately determine stability or otherwise in the latter case. Nomenclature A = see Eq. (13) and Fig. 3 anm, bnm = see Eqs. (32), (35) Cn = see Eq. (34) C = specific heat of STEM material El = bending stiffness of STEM section ec = coefficient of thermal expansion fn(r) = time varying part of u fn(s) = Laplace transform of/n(r) H = time independent part of temperature differential Ho = approximate average temperature h = see Eq. (5) J = time varying part of temperature differential J = Laplace transform of / k = conductivity Kt = thermal curvature Ki = time independent part of thermal curvature Kz = time varying part of thermal curvature Ko = see Eq. (17) I = length