This work develops models for the coupled structural-acoustic vibration of boundaries that reﬂect and transmit sound. First, the case of an inﬁnitely long, ﬂuid-loaded, sub-critical membrane that is periodically ﬁxed and forced by oblique incident acoustic waves is considered. The method of Analytical Numerical Matching (ANM) is extended to deal with the resulting spatially-periodic and discrete phase-shifted forcing. The high resolution content of the solution near the constraints is analytically treated with a polynomial known as the Local Solution. The remaining, rapidly converging, part of the solution is treated modally and is known as the Global Solution. The Composite ANM Solution is then determined for the motion of the structure, and the far-ﬁeld acoustic ﬁelds can be eﬃciently described. It is shown that the use of ANM eﬀectively addresses the sensitivity of the acoustic ﬁelds and structure motion to the accuracy of which the local region near the structural discontinuities is resolved.

The use of ANM is extended to demonstrate a method to deal with the mathematical diﬃculty of acoustic coincidence. The second module of this thesis presents ongoing work on the development of a model for a ﬂuid-loaded ﬁnite membrane in an inﬁnite baﬄe. Corrections to the in-vacuo structural wavenumber are developed to model the additional inertance and dissipative eﬀects of the surrounding ﬂuid media. The resulting dissipated energy as a function of frequency of the modiﬁed ﬁnite membrane is compared to energy radiated by the inﬁnite, periodically driven, ﬂuid loaded membrane to motivate further reﬁnements of the ﬁnite model.

### Selected References

Villa, M, and Bliss, DB. "Prediction of Reflection and Transmission by an Elastic Barrier with Periodic Structural Discontinuities Forced by Oblique Acoustic Waves" *The Journal of the Acoustical Society of America* 140, 3160. (2016).

Bliss, DB, Villa, M, and Franzoni, LP. "Prediction of Broadband High-Frequency Acoustic Reflection and Transmission from Subcritical Membranes and Elastic Plates" *The Journal of the Acoustical Society of America* 137, 2233. (2015).