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 lin e force and all other ribs are assumed to have infinite mechanical imp edance. Thus fluid loading provides the only mechanism for the transmi ssion of energy along the structure. Two forms of coupling arise in su ch a problem: local coupling, where energy is transmitted along the st ructure from rib to neighbouring rib, and long-range coupling, which r esults in direct coupling between the vibration source and more distan t ribs. In the absence of long-range coupling a stop/pass band frequen cy structure is established where, in a stop band, energy is exponenti ally localized around the source. The present study shows the importan ce of including long-range coupling in the problem and focuses on the response in stop bands. It is found, through direct numerical simulati ons and analytical calculations, that the strong exponential decay is ultimately replaced by a much slower algebraic decay. Different algebr aic decay laws are found to hold according to various fluid-loading re gimes and the size of the rib array. The effects of this change in beh aviour would have implications for structure-borne noise control in pe riodic fluid-loaded structures.