Dispersion of Axially Symmetric Waves in Composite, Elastic Rods

The dispersive characteristics of axially symmetric waves in infinitely long, composite, elastic rods are explored. The characteristic equation relating frequency to propagation constant is derived for 2‐material rods in which a solid, circular core of one material is bounded by and bonded to a circular casing of a second material of different physical properties. The equation is explored numerically using a digital computer for 2 rods displaying different geometric and physical properties. The lowest few branches of frequency spectra are developed from the roots of the equation, and the dispersive properties of the individual modes shown are discussed. The lowest few cutoff frequencies are established for each of the 2 rods, and the radial displacement distributions for each frequency is established. Finally, conditions are established for the existence of equivoluminal modes similar to those shown to exist in plates by Lamé and Lamb, in solid rods by Onoe, McNiven, and Mindlin, and in hollow cylinders by Gazis.