Torsional response of an elastic half space to a nonuniformly expanding ring source. (English) Zbl 0554.73020
Exact expressions for displacement in a homogeneous isotropic elastic half-space subjected to an impulsive torsional force spreading over the rim of a nonuniformly expanding ring source on the free surface are obtained in integral form. Both accelerating and decelerating expansion of the source have been considered. The analytic solution, in integral form, is obtained by the Cagniard De-Hoop technique. Different wave front surfaces with their region of existence have been shown. The first motion responses near different wave arrivals have been determined by a limiting process. The displacements on the free surface for different positions of the source have also been evaluated numerically and have been shown by graphs.
MSC:
| 74J10 | Bulk waves in solid mechanics |
| 35C15 | Integral representations of solutions to PDEs |
| 74S30 | Other numerical methods in solid mechanics (MSC2010) |
| 35L05 | Wave equation |
| 74J25 | Inverse problems for waves in solid mechanics |
Keywords:
displacement; homogeneous isotropic elastic half-space; impulsive torsional force; nonuniformly expanding ring source; accelerating and decelerating expansion; analytic solution; integral form; Cagniard De- Hoop technique; Different wave front surfaces; region of existence; first motion responses; limiting processReferences:
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