A Simple Method for the Analysis of Deep Cavity and Long Neck Acoustic Resonators

In this paper, deep cavity and long neck resonators are considered where one of the axial lengths is not significantly smaller than the sound wavelength . The axial motion of the fluid inside a deep cavity and the non-uniform motion of the fluid along a long neck are taken into account by means of linear or quadratic shape functions. In other words, the deep cavity or the long neck are represented by a simple one-dimensional finite element. Mathematical models of resonators having few degrees of freedom (d.o.f.) are developed and analytical expressions of the natural frequencies and impedances are derived. Calculated results are compared with predictions from one-dimensional acoustic theory and with experimental results.