Coupled tension–torsion vibration of repetitive beam-like structures

✍ Scribed by N.G. Stephen; Y. Zhang

• Publisher: Elsevier Science
• Year: 2006
• Tongue: English
• Weight: 325 KB
• Volume: 293
• Category: Article
• ISSN: 0022-460X
• DOI: 10.1016/j.jsv.2005.09.033

✦ Synopsis

Equivalent continuum stiffness properties, derived from the eigenanalysis of a single cell of a planar beam-like repetitive structure, have previously been employed within well-known dynamic theories, such as Euler-Bernoulli and Timoshenko for flexural vibration, suitably modified, to predict natural frequencies of vibration. Here the approach is applied to two structure types that exhibit tension-torsion coupling. The first is modelled on a NASA deployable structure with a crosssection of equilateral triangular form, but with asymmetric triangulation on the faces. The second is a related, more symmetric, structure but with pre-twist. The simplest tension-torsion dynamic theory due to Di Prima is employed, and this is extended to more general end conditions. This combined periodic structure/substitute continuum approach provides excellent agreement with predictions from the finite element method, especially for the lower modes of vibration; typically, agreement is within 71% for the lowest 8-10 natural frequencies for the longer, 30-cell structures considered here, the majority of these being torsional modes, and within 71% for the lowest 4-5 modes for the shorter, ten-cell, structures. This level of accuracy is attainable so long as a single wavelength spans 2-3 cells of the repetitive structure.