Anderson localization effects in the transmission of energy down an irregularly ribbed fluid-loaded structure

Abstract

The paper studies wave transmission along an infinite fluid-loaded elastic membrane supported by a finite array of irregularly spaced thin ribs, all having infinite mechanical impedance, except for the first, which is driven by a time-harmonic force. When the Green’s function of the unribbed structure is taken to consist only of its subsonic surface wave component, the response of the structure is exponentially localized (Anderson localization). A localization length is calculated, as a function of frequency, in both the small and the large disorder limits and in both of these limits the calculated localization length is found to agree extremely well with the results of numerical simulations. When a weak acoustic component is included in the Green’s function, it is shown that the exponential localization is short-circuited, the response now decaying algebraically with distance from the first rib, and with negligible sensitivity to disorder, even for rather large degrees of disorder.