The idea of treating a structural system in a statistical manner has been developed in order to understand the global response of the structure when many modes are excited. The statistical energy analysis (SEA) approach has been widely used for determining the dynamic response to broad band excitation of linear one and two dimensional structures and three dimensional internal acoustic fields. This project extends the method to (1) three dimensional solids, (2) external (unbounded) acoustic fields, (3) small scale, local structural nonlinearities and (4) SEA for coupled systems. In the first phase, the SEA result will initially be derived within the framework of a three dimensional, linear viscoelastic solid and then extended to a viscoelastic solid combined with a metallic structural foundation. In phase two, the Principal Investigator will use his previously developed SEA method for ascertaining the acoustic far field when a two dimensional structure is responding in many modes. The intent here is to compare this concept with the full classical modal result to determine the SEA method's range of applicability. In phase three, the classical component mode synthesis method is combined with SEA concepts to ascertain the global effects of nonlinearities on a structure when many modes have been excited. In phase four, the intent is to refine the methods currently available for determining loss factors between coupled systems. The impact of this work will be to permit a better description of the dynamics of complex dynamical systems which are responding in many degrees of freedom.
