LOCALIZATION AND DELOCALIZATION IN PERIODIC ONE-DIMENSIONAL DYNAMIC SYSTEMS

Abstract : The impulse response function of ribbed membrane-like panels is derived. A model of such a panel in which certain interactions among the ribs are removed is constructed. The removed interactions are those that allow a rib to identify the dispositions of the other ribs. It is argued that the impulse response function describing this model just fails, by definition, to account for the phenomena associated with pass and stop bands. The characteristics of this model are then used to explain the phenomenon of localization that occurs, at frequencies that lie within the pass bands, when the periodicity of the ribs is disturbed. Similarly, this model is used to explain the phenomenon of delocalization that occurs, at frequencies that lie within the stop bands, when the periodicity of the ribs is disturbed. The results of computer experiments that exhibit these types of localization are cited. Keywords: Localization; Ribbed panels; Periodic structures; Structural acoustics; Acoustic response of panels.