Geodesic
Propagation of longitudinal elastic waves in a rod surrounded by a medium of Winkler type
Vestnik Moskovskogo universiteta. Matematika, mehanika, no. 1 (1983), pp. 74-78

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We consider the propagation of longitudinal elastic waves of compression in a balf-endless uniform rod surrounded by a resisting medium. The rod has constant circular section and interacts with the medium according to the dry friction law, i. e. the magnitude of friction is proportional to the deformation of the rod. We find the exact solution of the corresponding problem when either the velocity or the loading of the particles in the end section is specified. We prove that the wave front goes to infinity. 
@article{VMUMM_1983_1_a18,
     author = {A. N. Filippov},
     title = {Propagation of longitudinal elastic waves in a rod surrounded by a medium of {Winkler} type},
     journal = {Vestnik Moskovskogo universiteta. Matematika, mehanika},
     pages = {74--78},
     publisher = {mathdoc},
     number = {1},
     year = {1983},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/VMUMM_1983_1_a18/}
}
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A. N. Filippov. Propagation of longitudinal elastic waves in a rod surrounded by a medium of Winkler type. Vestnik Moskovskogo universiteta. Matematika, mehanika, no. 1 (1983), pp. 74-78. http://geodesic.mathdoc.fr/item/VMUMM_1983_1_a18/