A broadband solid impedance transformer for acoustic transmission between water and air

Abstract

Broadband acoustic transmission between air and water can be obtained with a solid interface comprising three parallel thin elastic plates connected by two sets of parallel rigid ribs. Theoretical analysis combined with numerical optimization shows that the optimal 3-plate impedance transformer has a central plate far thicker than those facing air and water. This implies a simpler interpretation of the optimal 3-plate impedance transformer as two elastic plates separated by a mass-like impedance. The properties of the broadband transformer may then be understood using results for a previously studied 2-plate system and asymptotic approximations using the small air-to-water impedance ratio. Optimal systems with water and air-side plates of similar material have relative thicknesses of approximately three to one, respectively, with the central mass having areal density approximately 17 times the water side plate. Further identities relate the frequency of total transmission to the plate thicknesses and to the rib separation length. The impedance transformer is compared to an ideal two layer quarter wavelength model, allowing us to identify a minimal attainable Q-factor of about 5.5, which is achieved in examples presented. The explicit approximations to the optimized parameters also serve as the initial values for numerical optimization, greatly accelerating the process. Together, the theoretical and numerical results point to a remarkably simple class of purely solid impedance transformers, with system parameters well defined by the asymptotically small parameter: the ratio of air-to-water acoustic impedances.