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The asymptotic phase velocities, at very large wavenumbers, of nonaxisymmetric waves traveling in composite rods are established analytically. Frequency spectra and mode shapes of composite rods are presented and compared with those of simple (made of one material) rods.

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The frequency equation for trains of axisymmetric harmonic waves traveling in infinitely long three-layered circular cylindrical shells and rods is established on the basis of the three-dimensional theory of elasticity. The shells or rods are assumed to be made of three concentric cylinders, each of different isotropic material, bonded perfectly at their interfaces. The frequency equation has been evaluated numerically on an IBM 7044/7094 DCS system, and the effect of the geometric and physical parameters of the three-layered shells on the frequency of the first few modes is illustrated. The limits that the phase velocities of the various modes of propagation approach asymptotically at large wavenumbers are established analytically and verified by the numerical results.