| Summary: | This work considers the model problem of wave transmission along a fluid-loaded plane membrane supported by a finite number of equally spaced ribs with dynamic constraints. One of the ribs is driven by a prescribed time-harmonic line force applied uniformly along its length and the remaining ribs are passive. The steady-state, time-harmonic response of the ribs is investigated with particular emphasis on whether the disturbance is localized near the driving force and if so, at what rate the disturbance decays. Under the assumption of subsonic surface wave coupling only, which is explained in the text, closed-form solutions for the rib-forces are first obtained. The system is shown to exhibit a stop/pass band structure characteristic of one-dimensional periodic systems with lossless coupling between adjacent bays. The drive frequencies which define the band edges are ascertained and their dependence on the properties of the passive ribs is illustrated in detail. A critical rib mass is found at which the disturbances at the ribs vanish. The properties of the previously neglected acoustic (or hydrodynamic) coupling are then studied in order to determine the conditions under which the surface wave coupling approximation is appropriate. Some stop band solutions which include both surface wave and acoustic coupling are found which indicate the relative importance of the two types of coupling. Much of the analytical work is confirmed by numerical results and the methods used to derive these are explained.
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