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

Abstract

An approach base on group theory is described for calculating the eigenvalues and hence natural circular frequencies of vibration of cable nets consisting of two families of high 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 ndegrees of freedom in the form of vertical motions of masses concentrated at the cable intersections. After briefly outlining the linear cable net theory that forms the basis for the illustration of the proposed group-theoretic approach, those concepts of symmetry groups and representation theory that are fundamental to the present development are summarized. The actual computational scheme is then outlined, followed by a step-by-step illustration of the proposed procedure, the proposed method makes use of the full symmetry of the cable network in a systematic and highly efficient manner: the problem is decomposed into mutually independent subspaces spanned by symmetry adapted variables, for which the required eigenvalues are simply obtained through the solution of a small number of polynomial equations each of degree a fraction of n(instead of through the solution of a single polynomial equations of degree n, as yielded by a conventional analysis), resulting is substantial simplifications in the computation of the natural frequencies of vibration of the cable network. Once eigenvalues have been obtained, calculation of the system eigenvector components is carried out on the basis of parent subspaces of the eigenvalues, with mode shapes of the cable net following through a relatively trivial final step.