High frequency asymptotic analysis

The propagation of guided circumferential waves in a circular elastic annulus is studied, and both SH and Lamb-type modes are considered. By using various asymptotic techniques (asymptotic reduction of the exact dispersion relation, ray methods and WKBJ analysis), we derive simple and very rapidly evaluated, asymptotically accurate dispersion relations, and reveal completely the underlying ray structures of various modes in the annulus. Several types of modes, not existing in a straight plate, have been identified; in particular, these include modes possessing a caustic of longitudinal or shear rays inside the annulus, and whispering-gallery-type modes. Comparisons of dispersion curves evaluated from the exact and asymptotic dispersion relations are presented. The typical error is less than 0.2% except for the very low frequency region; the asymptotic code is an order of magnitude faster and more stable at high frequencies.

Co-authored with Dmitri Gridin, Jimmy Fong, Mike Lowe and Malcolm Beard.

Wave Motion, 38, 67--90, 2003