Global and local partial response of ribbed uniform panels

Abstract

Two formalisms of the response of a ribbed uniform panel excited by a line drive are considered. In the first, the global response is obtained. In this response, phases among the responses of the bays are preserved and accounted for. (A bay is the portion of the panel that lies between two adjacent ribs.) The preservation of the phases yield responses that exhibit the phenomena of pass and stop bands and of localizations and delocalizations when the separations between adjacent ribs are equal. In the second formalism, the local response is obtained. The response is estimated in terms of the energy densities in the individual bays. In this formalism the phases among the responses of the bays are inconsequential. Therefore, the phenomena of pass and stop bands and of localizations and delocalizations are not manifested in the localized response. It is thus suggested that formalisms that are akin to the statistical energy analysis (SEA) and SEA itself cannot be expected to exhibit some of the features in the response of a complex structure, especially if the structure is composed of a number of regular substructures; e.g., the identical bays in a ribbed panel. Generic examples are presented in this paper to illustrate that in certain situations and for certain purposes the missing features in the local response, as compared with the global response, may be significant.