A simplified method for approximating the natural frequencies of acoustic-structure systems

Abstract

It is well known that the natural frequency of a flexible structure in contact with a fluid-filled cavity can be approximated with a closed-form expression that considers the coupling of only two component modes (i.e., a rigid-wall acoustic mode and an in vacuo structural mode) [F. Fahy, Sound and Structural Vibration (Academic, London, 1985), Chap. 6, pp. 249–256]. However, this expression requires volume and area integrations over the component mode shapes. For many practical configurations, the effort to determine the component mode shapes and compute the necessary integrals counteracts much of the time and computational savings afforded by the closed-form expression. Here, the closed-form expression is recast as a function of the nondimensional frequency separation between the component modes and a new nondimensional coupling parameter, Ψ. Design curves representing the value of Ψ for common geometries and boundary conditions are presented. With the use of these design curves and a knowledge of the component modes frequencies, one can quickly compute reasonable approximations of the coupled natural frequencies by hand.