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Transmission of energy down periodically ribbed elastic structures under fluid loading: algebraic decay in the stop bands

The paper examines the role played by long–range acoustic coupling in the transmission of energy down a periodically ribbed elastic membrane under fluid loading. One of the ribs is driven by a time–harmonic line force and all other ribs are assumed to have infinite mechanical impedance. Thus fluid loading provides the only mechanism for the transmission of energy along the structure. Two forms of coupling arise in such a problem: local coupling, where energy is transmitted along the structure from rib to neighbouring rib, and long–range coupling, which results in direct coupling between the vibration source and more distant ribs. In the absence of long–range coupling a stop/pass band frequency structure is established where, in a stop band, energy is exponentially localized around the source. The present study shows the importance of including long–range coupling in the problem and focuses on the response in stop bands. It is found, through direct numerical simulations and analytical calculations, that the strong exponential decay is ultimately replaced by a much slower algebraic decay. Different algebraic decay laws are found to hold according to various fluid–loading regimes and the size of the rib array. The effects of this change in behaviour would have implications for structure–borne noise control in periodic fluid–loaded structures.