Matched Asymptotic Expansion (MAE) technique applied to acoustic radiation from vibrating surfaces

Abstract

The MAE technique has been used in the field of fluid mechanics for many years. Only recently has this technique been applied to acoustic problems, where it has been found to be an excellent and powerful tool in analyzing either scattering and diffraction or radiation from moving rigid objects (propellers). In this paper it is shown how the MAE technique can be utilized to solve acoustic radiation problems from flexible surfaces. The technique is then applied to the following force driven systems: (1) circular piston in infinite rigid baffle, (2) two concentric pistons in infinite modes. For each of problem analyzed, the structural wavelength a is assumed to be small compared to the fluid wavelength (i.e., ka ≪ 1). The inner region close to the vibrating structure (acoustic boundary layer) is governed by the Laplace's equation while the outer solution is governed by the Helmholtz equation. The inner and outer solution is governed by the Helmholtz equation. The inner and outer solutions are solved independently and are then joined together by the MAE matching procedure. A composite solution is then obtained from a combination of the inner and the outer solution. Agreements with the exact theory for the radiated pressure, surface resistance, and reactance are shown to be excellent.