Localization of vibrations in large space reflectors

Abstract

A study is presented of the mode localization phenomenon in a generic class of large space reflectors. The study is based on a Rayleigh-Ritz formulation using the first five cantilevered beam bending modes and a finite-element formulation using Bernoulli-Euler beam elements. Coupling between the structures is provided by massless axial members. Numerical results indicate that mode localization does, in fact, occur in engineering structures of this type. Localization is characterized by the amplitude of a global mode becoming confined to a local region of the structure. For the 18-rib reflector studied, the first rib bending mode did not localize, but the second and third modes did. Localization is found to become more severe with increasing mode number. Increasing the number of ribs to 48 resulted in significant distortion in some of the first rib bending modes and severe localization of the second and third bending modes. The phenomenon of wave confinement in finite structures is also demonstrated using a single-degree-of-freedom per substructure model. Nomenclature