Supplementary file for manuscript Ultrasonic Torsional Wave Excitation Using Double-layer Flexible Magnetostrictive Transducer for High Density Polyethylene (HDPE) Pipes Detection

This is a supplementary files collection of papers to a manuscript submitted to the IEEE TII Journal entitled "Ultrasonic Torsional Wave Excitation Using Dou-ble-layer Flexible Magnetostrictive Transducer for High Density Polyethylene (HDPE) Pipes Detection". The manuscript is limited in space and much of the work could not be placed in it, only some of the important elements are included. Therefore, some relatively less important work has been placed in this document to allow reviewers and readers to have a more detailed understanding of our work and ideas. Please contact us if there is anything you would like to know more about.