Propagation constants from the response of a finite periodic beam

Abstract

An infinite periodic structure is usually modeled using a single span with appropriate periodic conditions. If a large finite periodic structure with N spans behaves like an infinite periodic structure, then, here also a single span model will suffice giving cost savings in computation. This paper is about such a meeting point between infinite and finite periodic structures. The propagation constant of an infinite periodically supported beam is obtained analytically from the response of a finite periodically supported beam. In an infinite periodic beam, e g (g is the complex propagation constant) is the ratio of velocities in any two neighboring spans and is obtained using a single span model. Here, it is shown (analytically and experimentally) that if the finite periodic beam has enough spans, then eg computed from the first two spans will match eg for an infinite periodic beam in the attenuation zones.