Stephen, N.G. and Zhang, Y.
Eigenanalysis and continuum modelling of an asymmetric beam-like repetitive structure
International Journal of Mechanical Sciences, 46, (8), . (doi:10.1016/j.ijmecsci.2004.07.012).
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An asymmetric repetitive pin-jointed structure, based upon a 3-D NASA framework, is analysed using a state variable transfer matrix technique. A conventional transfer matrix cannot be constructed due to the singularity of one partition of the stiffness matrix; instead, a cell (rather than cross-sectional) state vector consisting of displacements only is employed, leading to a generalised eigenvalue problem. The asymmetry of the structure leads to tension–torsion and bending–shear couplings, which may be explained in terms of the tension–shear coupling of a single face of the structure. Equivalent continuum beam properties and coupling coefficients are determined, and the effect of (a)symmetry discussed as a trade between, for example, tension-Poisson's ratio contraction for a symmetric structure, against tension–torsion coupling for the asymmetric.
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