Abstract
Reflection characteristics of longitudinal strain waves in a semi-infinite cylindrical rod connected to an infinite elastic stratum are investigated analytically. Applying three-dimensional elasticity theory to the stratum and making use of Laplace transformations with respect to time and numerical inverse Laplace transformations, the time histories for the longitudinal strain at an arbitrary point of the rod are presented. Numerical results obtained from three-dimensional elasticity theory are compared with numerical results obtained from Mindlin plate theory, classical plate theory, and experimental results. When the stratum is stiff compared with the rod, the reflected waves from the interface between the stratum and the rod, which are obtained from the three theories, i.e., three-dimensional elasticity theory, Mindlin plate theory, and classical plate theory, are nearly coincident with one another. On the contrary, when the stratum is flexible compared with the rod, they are different from one another. The stratum may be considered as a half-space for a stratum thickness ratio (stratum thickness/rod radius) κ≥8.0 in the case of the stiff stratum, while it may be considered as a half-space for κ≥15.0 in the case of the flexible stratum.
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