A Fourier series solution for the radiation impedance of a finite cylinder

Abstract

A mathematical model for the radiation impedance of a finite cylinder with extended rigid ends is developed using a Fourier series approach. This series approach is shown to be possible by modeling the cylinder as a widely separated periodic replica representation. Radiation impedance results are obtained for the cylinder operating in uniform, dipole, and cardioid radial modes of vibration. The cardioid mode is then used as a radiation impedance model for the underwater sound slotted cylinder transducer.