Location of Repository

Coupled tension-torsion vibration of repetitive beam-like structures

By N.G. Stephen and Y. Zhang

Abstract

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 cross-section 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 ±1% for the lowest 8–10 natural frequencies for the longer, 30-cell structures considered here, the majority of these being torsional modes, and within ±1% 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

Topics: TA, QC
Year: 2006
OAI identifier: oai:eprints.soton.ac.uk:23693
Provided by: e-Prints Soton

Suggested articles

Preview

Citations

  1. (1998). A review of current analysis capabilities applicable to the high frequency vibration prediction of aerospace structures,
  2. (1996). A transfer matrix analysis of the energetics of structural wave motion and harmonic vibration,
  3. (1944). A Treatise on the Mathematical Theory of Elasticity,
  4. (1985). Comparison of dynamic torsion theories for beams of elliptical cross-section,
  5. (1998). Continuum modelling for repetitive lattice structures,
  6. (1959). Coupled torsional and longitudinal vibrations of a thin bar,
  7. (1976). Discrete Field Analysis of Structural Systems,
  8. (1989). Dynamics of complex truss-type space structures,
  9. (2005). Eigenanalysis and continuum modelling of a curved repetitive beam-like structure,
  10. (2004). Eigenanalysis and continuum modelling of an asymmetric beam-like repetitive structure,
  11. Eigenanalysis and continuum modelling of pre-twisted repetitive beam-like structures.
  12. (1995). Energy partitioning in a truss structure,
  13. (1970). Free wave propagation in periodically supported infinite beams,
  14. (1972). Introduction to the Finite Element Method,
  15. (2004). Mid and high-frequency vibration analysis of structures with uncertain properties.
  16. (1996). On Saint-Venant’s principle in pin-jointed frameworks,
  17. (1995). On the direct solution of wave propagation for repetitive structures,
  18. (1999). On the vibration of one-dimensional periodic structures,
  19. (1957). On torsional vibrations of a beam with a small amount of pretwist,
  20. (1989). Propagation of decaying waves in periodic and piecewise periodic structures of finite length,
  21. (1977). Response of periodic structures by the z-transform method,
  22. (1991). Structural and dynamic behaviour of pretwisted rods and beams,
  23. (1984). The beam-like behaviour of space trusses,
  24. (1951). The effect of initial twist on the torsional rigidity of thin prismatic bars and tubular members,
  25. (1992). Wave problems for repetitive structures and symplectic mathematics,
  26. (1996). Wave propagation in continuous periodic structures: research contributions from Southampton,

To submit an update or takedown request for this paper, please submit an Update/Correction/Removal Request.