Vibration and Large Deflection of Cantilevered Elastica Compressed by Angled Cable

• Published in: AIAA journal 2006-07, Vol.44 (7), p.1468-1476
• Main Authors: Holland, David B, Stanciulescu, Ilinca, Virgin, Lawrence N, Plaut, Raymond H
• Format: Article
• Language: English
• Subjects: Aerodynamics; Equilibrium; Exact sciences and technology; Finite element analysis; Fundamental areas of phenomenology (including applications); Numerical analysis; Physics; Solid mechanics; Structural and continuum mechanics; Vibration; Vibration, mechanical wave, dynamic stability (aeroelasticity, vibration control...)
• ISSN: 0001-1452; 1533-385X
• DOI: 10.2514/1.18000

A thin cantilevered beam is compressed by a cable attached to the tip of the beam and terminating near the base. Large-deflection equilibrium configurations and small vibrations about equilibrium are investigated. This system has a direct application to solar-sail structures, where the structural booms could be designed to bend to supply tension loading in the sail membrane. The equilibrium and vibration properties are examined in three ways: numerical integration of the governing elastica equations using a shooting method, finite element analysis using ABAQUS, and experiments with a polycarbonate strip bent by a cable that is tightened with a turnbuckle. Equilibrium shapes and vibration mode shapes and frequencies are obtained for two different cable attachment points offset slightly from the beam's base in the axial and transverse directions. Frequencies obtained from a three-dimensional finite element analysis are also presented.