Circuit models for thermoviscous acoustics in waveguides of various cross sections via continued fractions.

Abstract

Thermal and viscous losses are crucial for accurate representation of wave propagation in small conduits. Analytical expressions exist for the series and shunt immitances representing the transmission line characteristics of thermoviscous acoustics in one-dimensional tubes of certain cross sections, and for a subset of these cases, circuit models with constant and positive component values can approximate these generally nonrational solutions. A continued fraction approach introduced previously for the circular cross section has been applied, here, to the slit and equilateral triangular cross-section cases with the same canonical forms and constant and positive component values for the series and shunt immitances. The resulting networks can be used for steady-state and time-dependent calculations due to their passivity and rational nature and are easily expanded to cover any desired frequency range.