On the use of a variational technique based on integral equations for plane acoustic and vibro-acoustic problems

Problems such as sound insulation and absorption of plane structures in laboratory conditions can theoretically be described as an integral or integral-differential equation. This equation contains the Green’s function integrated over the surface, which describes the radiation from the surface. A variational technique, well described by Morse and Ingard, has successfully been used for both absorption and sound insulation for a plane incident wave.

The resulting formulas are surprisingly simple, accurate and robust. Moreover, they capture the physics of sound radiation of a finite surface well. However, the approach has turned out problematic in more complicated cases, including spatial periodicity. The paper discusses these issues, and suggests modifications to overcome the problems.