Transient Response of an Inhomogeneous Elastic Hollow Cylinder to an Impulsive Line SH-source

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This paper considers the two-dimensional wave propagation in an inhomogeneous elastic hollow cylinder. Art impulsive line SH-source is placed in the hollow cylinder. Its inhomogeneity is assumed such that rigidity μ and density ρ vary with radial distance γ from the center of the cylinder as μ=μ_0 (γ/α)^λ, ρ=ρ_0(γ/α)^<λ-2>, and then SH-wave velocity increases linearly with distance γ; C=C_0γ/α. An exact solution is obtained in closed form with an application of the ray expansion technique. It is found that a disturbance caused by waves reflected even times at the boundaries much resembles to one caused by the direct wave from the source. This similarity may be called the wave form equivalence. Some numerical computations are carried out to show that the stress response at the inner boundary of the hollow cylinder is more sensible to the variation of inhomogeneous parameter λ than that at the outer boundary.
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