A rapid technique to determine the internal area function of finite-lengthducts using maximum length sequence analysis

This paper describes a rapid technique for reconstruction of the internal a rea function of a duct using blockage-induced eigenvalue shifts determined from eigenfrequencies measured under two sets of duct termination boundary conditions. A single broad band maximum length sequence (MLS) measurement o f short duration is utilized to obtain the transfer function of the duct, w hich in turn can be utilized to determine its eigenvalue shifts and subsequ ently its internal area function using an inverse perturbation technique. T he reconstruction results display the same order of accuracy as those obtai ned previously using swept sine measurements of extended duration. An expre ssion for the determination of the area function is presented utilizing res onant frequency information alone, thus rendering duct length determination unnecessary. A computational routine further simplifies the process such t hat the accuracy of the technique could be ascertained for a range of confi gurations including longer ducts and ducts that initially have nonuniform i nternal cross section over their length. Development of a relationship betw een obstacle length and wavelength of the lowest eigenfrequency required fo r successful reconstruction is also described. This is an important result for longer ducts where measurement of lower eigenfrequencies may present pr oblems using standard measurement equipment. (C) 2000 Acoustical Society of America. [S0001-4966(00)00907-3].