Propagation of Harmonic Waves in Composite Circular-Cylindrical Rods

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Abstract
In this investigation, the general frequency equation for harmonic waves having an arbitrary number of circumferential nodes, traveling in composite traction‐free, circular‐cylindrical rods is established on the basis of the linear three‐dimensional theory of elasticity. The composite rods consist of a circular core made of one material, bounded by and bonded to a circular casing of another material. Simpler degenerate cases of the frequency equation are reduced and discussed. A numerical evaluation of the frequency equation is presented. The results are obtained by programming an iteration procedure on a digital computer. The effect of the variation of the physical and geometric parameters of the rod on the frequencies and mode shapes of the first few modes is illustrated and discussed. Moreover, the feasibility of utilizing composite rods as delay media in guided‐wave ultrasonic delay lines is considered briefly.

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