Vibration Characteristics of Asymmetric Flexible Cantilever Beams Connected to a Central Rigid Body

Abstract

A satellite with two solar wings can be modeled using a pair of symmetric flexible cantilever beams connected to a central rigid body. Due to certain reasons, the symmetric flexible cantilever beams may be turned into asymmetric ones, which will inevitably influence the vibration properties of the structural system. By changing the structural sizes and adding local mass on one side of the two beams, a structural system with asymmetric mass distribution is obtained and its vibration characteristics are investigated. Hamilton’s principle with the assumed mode method is employed to establish the equation of motion of the asymmetric structural system. The natural frequencies, mode shapes, frequency response curves and displacement time histories of the system are calculated, and they are compared with those of the structural system with a symmetric mass distribution. The correctness and feasibility of the present analytical method are verified by means of the finite element method (FEM) and a vibration experiment. The analytical results show that the mass asymmetry of the two beams leads to the mode localization phenomenon, and the coupling effect between the two beams and the central rigid body is enhanced. The larger the mass asymmetry is and the closer the position of the added local mass to the end of the cantilever beam is, the more obvious of the mode localization phenomenon is and the more obvious of the coupling effect between the two beams and the central rigid body is. The present investigation results are helpful for the dynamic analysis and design of spacecraft structures composed of flexible solar wings and a central rigid body.

Keywords

• asymmetric flexible cantilever beams
• central rigid body
• Hamilton’s principle
• assumed mode method
• mass asymmetry
• vibration characteristics