In this study, the acoustic resonance scattering is dealt with for the multilayered cylindrical structures immersed in a fluid. The theoretical model has been generally developed from the global matrix formulation for the acoustic scattering of multilayered structures with elastic-elastic, elastic-fluid and fluid-fluid interfaces. The concept of the boundary matrix is introduced to facilitate the generalization of the multilayer model. The boundary matrix represents the wave field of each layer, satisfying the boundary conditions at the outer and inner boundaries. The boundary matrices of all interfaces can be assembled to the diagonal banded global matrix of the multilayered cylindrical structures, which represents the complete scattering system. The global matrix formulation is applicable to any cylindrical system with an arbitrary number of layers for any sequence of solids or fluids. The individual element of the boundary matrices for the various layered systems are thus expressed as generalized forms.
For the scattering of acoustic waves by an elastic shell, the acoustical background coefficients are inherently incorporated in the scattering coefficients. The background coefficients for the elastic empty shells, so called the "inherent background", can be obtained from the zero-frequency limit of the modal accelerance in the scattering functions for analogous liquid shells. The methodology of the previous work of obtaining the inherent background is extended to multilayered, elastic, cylindrical structures. The inherent background can be identified from the sound scattering by the liquid structures. The scattering S-function and the modal accelerance of the liquid system are determined and generalized such that the scattering function can be obtained by the recurrence relation for the accelerance of the adjacent liquid layers. From the zero frequency limit of the generalized accelerance of liquid structures, the general expression of the inherent background coefficients is obtained. The background coefficients depend on the densities of the layers and the ambient fluid medium, the relative thickness of each layer and the normal mode number. The acoustical background coefficients for solid cylinders, empty shells, fluid-filled shells and double-layered shells can be analytically obtained by the appropriate limit of the density ratio and relative thickness of layers in the generalized inherent background coefficients. The usefulness of the proposed background is demonstrated for several examples of layered structures.
As an application example and for the verification of the theory, the acoustic resonance scattering from the 12% thick Zr shells coated with zirconium oxide ($ZrO_2$) layers and the equivalent bare Zr shells has been investigated by the numerical analysis and confirmed through the experiment. The change of the phase velocity of the $A_1$ circumferential wave mode for the coated Zr shell is negligibly small at n = 15 and n = 16 partial waves, in spite of the presence of the $ZrO_2$ layer and the increase in coating thickness. The $ZrO_2$ layer thickness of the coated Zr shell can be experimentally estimated using the invariable characteristic of the phase velocity of the $A_1$ mode. The phase velocity of the $S_0$ circumferential wave mode for the coated shells is faster than that of the equivalent bare Zr shells. The phase velocity of the $S_0$ mode for the coated shells is mainly influenced by the velocity of the coating material. The phase velocity of the momentless $S_0$ mode for bare shells do not vary for the modes below n = 13 partial waves, in spite of the fact that the shell thickness and inner/outer diameters are slightly changed. Utilizing the invariability condition of the phase velocity of the $S_0$ mode, the subtle variance of the mean diameter of bare shells can be measured. The shell thickness can be measured by using the thickness resonance. In this way, the new nondestructive techniques for the relative measurement of the dimension of bare shells and the coating thickness of coated shells have been proposed.