Abstract
A fundamental matrix theory is developed for the exact isolation (in both magnitude and phase) of resonance amplitudes contained in the elastic field scattered by a penetrable target. Similarities and differences between this matrix theory and the classical resonance scattering theory [L. Flax, L. R. Dragonette, and H. Uberall, J. Acoust. Soc. Am. 63, 723–731 (1978)] are discussed. The matrix theory is then applied to cylindrical and spherical fluid-filled cavities, and analytical expressions for the resonance amplitudes are derived. In the vicinity of resonance frequencies, the resonance amplitude expressions have forms similar to the Breit–Wigner formula. In order to check the validity of the matrix theory, numerical calculations are performed for a cylindrical water-filled cavity in an aluminum medium. Resonance spectra of the cavity are presented for some partial waves and their characteristics are also discussed.
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