Effect of an isolated irregularity on the transmission of energy down a periodically ribbed fluid-loaded elastic structure

Abstract

The paper considers the problem of wave transmission in a configuration consisting of an infinite fluid-loaded elastic membrane supported by a finite array of thin ribs. The ribs are equally spaced except for one which is randomly displaced from its periodic location by a small amount. One of the ribs (not the displaced one) is driven at a prescribed velocity by a time-harmonic force, and all the others are held at rest (they are assumed to have infinite mechanical impedance) so that fluid loading provides the only mechanism by which energy can be transmitted down the ribbed part of the structure. An exact solution for the forces exerted on the membrane by the ribs is obtained in terms of the eigenvalues and eigenvectors of a 2 x 2 propagation matrix and the solution is shown to be consistent with energy conservation requirements. It is found that the random displacement of one rib leaves the response in the stop bands almost unchanged (including the response at the displaced rib), but has a large effect in the pass bands. There the energy transmitted to infinity beyond the displaced rib is dramatically reduced. Two effects contributing to this are first that the input power to the irregular configuration is generally less than that to the regular one, and second that the array of regular ribs with one isolated irregularity is found to reflect most of the energy incident on it from the driven rib (provided the degree of irregularity is not too small and provided that the frequency does not lie in one of a small number of narrow bands of high transmission).