Taut cables with hanging masses: A metamaterial-like dynamic behavior

Abstract

We inspect the dynamic behavior of suspended cables presenting a periodic array of scatter elements, consisting of a discrete set of masses that are hanging by means of elastic or rigid connections. By introducing some approximations, we show that the problem in the continuous domain can be brought back to an equivalent discrete problem, whose solutions depend on the variation of an effective mass. We find that the essential spectrum of the problem presents band gaps. By considering boundary conditions, eigenmodes can only be found at frequencies belonging to pass bands for the propagation problem of the unbounded system. This is no more true when a defect of periodicity is inserted, leading to the formation of localized modes. We provide a quantitative validation of these theoretical results by means of comparison with experimental tests.