On Dowell’s simplification for acoustic cavity-structure interaction and consistent alternatives

A widely employed description of the acoustical response in a cavity whose walls are compliant, which was first proposed by Dowell and Voss [(1962). AIAA J. 1, 476–477], uses the modes of the corresponding cavity with rigid walls as basis functions for a series representation of the pressure. It yields a velocity field that is not compatible with the movement of the boundary, and the system equations do not satisfy the principle of reciprocity. The simplified formulation is compared to consistent solutions of the coupled field equations in the time and frequency domains. In addition, this paper introduces an extension of the Ritz series method to fluid-structure coupled systems that satisfies all continuity conditions by imposing constraint equations to enforce any such conditions that are not identically satisfied by the series. A slender waveguide terminated by an oscillator is analyzed by each method. The simplified formulation is found to be very accurate for light fluid loading, except for the pressure field at frequencies below the fundamental rigid-cavity resonance, whereas the Ritz series solution is found to be extremely accurate in all cases.