The response of two-dimensional periodic structures to point harmonic forcing

This analysis is concerned with the response of an infinite two-dimensional periodic structure to point harmonic loading; initially a damped finite system is considered and the system size is then allowed to tend to infinity. It is shown that the response in the far field can be expressed in terms of the properties of the ''phase constant surfaces'' which arise in the analysis of plane wave motion through the system. Within a pass band it is found that the physical nature of the response is strongly affected by the presence or otherwise of a caustic. In the absence of a caustic the response amplitude has a relatively smooth spatial distribution; if a caustic is present then the response amplitude has a complex spatial pattern and a ''dead region'' of very low response occurs. The theory is applied to a two-dimensional mass/spring periodic system and a comparison is made with an exact calculation for the response of a large finite system-excellent agreement is obtained between the two sets of results. The work has application to all types of two-dimensional periodic structures, including orthogonally stiffened plates and shells, and it raises the possibility of designing a periodic structure to act as a spatial filter to isolate sensitive equipment from a localized excitation source. (C) 1996 Academic Press Limited