A simplified approach for predicting interaction between flexible structures and acoustic enclosures

- A nondimensional expression for acoustoelastic natural frequencies is derived.
- A nondimensional number quantifying coupling between component modes is defined.
- The nondimensional number is calculated for different mode pairs in common geometries.
- Examples show how accurate acoustoelastic frequencies can be calculated by hand.

The natural frequencies of acoustic-structure systems can be approximated by a closed-form expression that accounts for the interaction between two uncoupled component modes: a given structural mode and the acoustic mode with which it couples most strongly. This expression requires spatial integration of the component mode shapes. In practice, the effort to determine the component mode shapes and compute the necessary integrals negates the simplicity afforded by the closed-form expression. Here, with the use of coupled mode theory, a new nondimensional expression for the coupled natural frequencies is derived. The derivation includes the definition of a new dimensionless number that quantifies the natural propensity of two component modes to couple, irrespective of the enclosure size or the fluid and structural properties. Values of this dimensionless number are presented for common geometries and boundary conditions. With these values, approximations of the coupled natural frequencies can be calculated by hand without explicit knowledge of the component mode shapes or their spatial integrals. The accuracy of these hand calculations is shown for two common acoustic-structure systems: a plate coupled to a rectangular air-filled enclosure and a cylindrical shell containing water.