AN EFFICIENT COMPUTATIONAL SCHEME FOR THE VIBRATION ANALYSIS OF HIGH-TENSION CABLE NETS

An approach based on group theory is described for calculating the eig envalues and hence natural circular frequencies of vibration of cable nets consisting of two families of highly tensioned cables, each cable lying in a vertical plane, and with the projections of cables on the horizontal plane comprising two perpendicular sets of lines. The cable net systems are assumed to have n degrees of freedom in the form of v ertical motions of masses concentrated at the cable intersections. Aft er briefly outlining the linear cable net theory that forms the basis for the illustration of the proposed group-theoretic approach, those c oncepts of symmetry groups and representation theory that are fundamen tal to the present development are summarized. The actual computationa l scheme is then outlined, followed by a step-by-step illustration of the proposed procedure through two examples. Compared with the convent ional procedure, the proposed method makes use of the full symmetry of the cable network in a systematic and highly efficient manner: the pr oblem is decomposed into mutually independent subspaces spanned by sym metry adapted variables, for which the required eigenvalues are simply obtained through the solution of a small number of polynomial equatio ns each of degree a fraction of n (instead of through the solution of a single polynomial equation of degree n, as yielded by a conventional analysis), resulting in substantial simplifications in the computatio n of the natural frequencies of vibration of the cable network. Once e igenvalues have been obtained, calculation of the system eigenvector c omponents is carried out on the basis of parent subspaces of the eigen values, with mode shapes of the cable net following through a relative ly trivial final step. (C) 1996 Academic Press Limited