Abstract
One dimensional equations of motion are obtained for axially symmetric torsional deformation in elastic, composite cylinders. Under consideration are cylinders composed of two materials: a circular inner core surrounded by an annulus of different material properties. These approximate equations were obtained from the variational equations of motion of a linear elastic medium by assuming a set of simple, orthogonal displacement functions. These functions were chosen to give the first two branches of the dispersion diagram for torsional waves in the composite cylinder. The slope of the first branch at the origin of the dispersion diagram is identical with the corresponding slope obtained from the “exact” analysis. Two correction factors are introduced in the approximate equations in order for the second branch to match the exact analysis at two particular points. The dispersion relations obtained from the resulting corrected equations are very accurate through a wide range of frequencies for real wave numbers. Conditions at the end of finite cylinders, sufficient to provide a unique solution, are provided.
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