An approximation to the local acoustic impedance of a cylindrical shell with hemispherical endcaps

A method has been developed to approximate the local radiation impedance of a cylindrical shell with hemispherical endcaps. This approximation greatly reduces the effort required to calculate the acoustic impedance as compared to an approach using a variational method. The approximate method uses the exact acoustic impedances of several separable geometric shapes to approximate the acoustic impedance of a complex structure that is a composite of those shapes. The shell is broken into three components: two hemispheres and a finite cylinder. These components are parts of regions that are separable in an orthogonal coordinate system. It is assumed that the acoustic impedance of the components is the same as the acoustic impedance calculated exactly for the separable shapes. Furthermore, it is assumed that the local acoustic impedance of the original complex shape is the same as that of corresponding points on the simple components. The accuracy is improved when the interaction between neighboring components is considered. The acoustic impedance and surface pressure generated by a load applied in the center of the complex shape is compared with that calculated using a variational formulation.