Dispersion of Flexural Waves in Circular Bimaterial Cylinders—Theoretical Treatment

The general form for displacements and the frequency equation are obtained for the first mode of flexural wave propagation in an infinitely long circular bimaterial cylinder. Based on the equations of linear elasticity, the theory follows the technique developed by Pochhammer and Chree for elastic bars. Several first-branch dispersion curves for the first flexural mode are presented for various ratios of the constituent cylinder radii. Dispersion characteristics significantly different from those predicted by the theory for homogeneous cylinders are realized. Some implications in regard to equivalent properties are discussed.