Filtration of Elastic Waves in Solid Rods with Membranes as Side Branches

Abstract

This paper considers theoretically the propagation of compressional and torsional waves in solid rods having membranes as side branches. An infinite cylindrical rod is loaded at equal intervals with flexible circular membranes attached at their outer edges to the inside of a circular cylinder (see Fig. 1). The assumption that longitudinal waves in the rod set up symmetrical transverse waves in the membranes leads to the conclusion that the structure is a high-pass compressional wave filter. The limiting case of an infinitely rigid membrane is also investigated. There is next considered the case of torsional waves in the rod giving rise to radial torsional waves in the attached membranes which now may be treated either as flexible or rigid diaphragms. When the latter are rigidly clamped at their outer edges, the structure is found to be a high-pass torsional wave filter. When the diaphragms are free at the outer edges, a low-pass filter results. The transmission characteristics are given for each case along with numerical illustrations.