Vibrations in Three Interconnected Regions: Membranes or Acoustic Cells

A method is given to estimate the power transmitted from one membrane to another in the case of three partially joined membranes, undergoing small amplitude transverse oscillations, when one of the membranes is excited by a point force and the lengths of the two common joins between adjacent membranes is small compared with a typical dimension of the membranes. The problem is equivalent to that of an acoustics problem forced by an oscillatory line source and the language of acoustics is used. A matching technique is used as well as an integral equation method. These give the same results to first order and agree well with numerical calculations. The integral equation method can be extended to higher order and both techniques can be extended to deal with more than three interconnected membranes or acoustic regions.