The application of two-dimensional signal transformations to the analysis and synthesis of structural excitations observed in acoustical scattering

Acoustic scattering from air-filled, elastic shells submerged in water is an important problem in applied science. The excitations of interest yield a set of physically distinct components to the impulse response of a shell. The components form a natural basis for all signals which can be observed in acoustical scattering experiments from the shell via temporal convolution with some chosen input signal. The Fourier transform (FT) of the impulse response of a shell yields its transfer function, which is also called the form function. We study two types of shells in this paper: a spherical shell, and a finite, ribbed, cylindrical shell with endcaps. Utilizing several different two-dimensional (2-D) signal transformations, we can decompose the response of the shells. The resulting 2-D images allow for a striking visual decomposition of the responses into their distinct components. In the case of the spherical shell, a virtually exact theory exists that allows for analytic synthesis of the shell response into its components. However, for the more complex cylindrical shell, the theory for the direct scattering problem is not nearly so mature. Yet, we can still decompose experimentally-obtained shell responses into their distinct components via signal synthesis techniques applied to the 2-D transforms