A boundary-field integral equation for analysis of cavity acoustic spectrum

The acoustic spectrum of cavities can be identified using integral equation formulations. Because of the transcendental dependence on frequency of the Green function, difficulties arise in calculating acoustic frequencies and modes of vibration when the Kirchhoff–Helmholtz boundary-integral operator is applied. This trouble is circumvented by the present, nonstandard, integral formulation that, by using the fundamental solution of the Laplace operator, allows the identification of acoustic spectra of cavities through solution of a standard eigenvalue problem. This formulation is compared both with that based on the Kirchhoff–Helmholtz operator and with an alternative integral approach introduced in the past that, akin to the one used here, analyzes cavity acoustics in terms of an eigenvalue problem. The numerical investigation deals both with a simple box-shaped cavity and with cavities related to applications of aeronautical interest.