Abstract
Wave propagation and vibration of elastic rods interacting with their environment according to the Coulomb dry friction law, are studied. Exact solutions of the nonlinear problems of impact of semi-infinite or finite rods, with constant stress and velocity or by a rigid body are obtained. Problems of smooth loading and unloading of a semi-infinite rod are solved as well. A method of exact analytical solution of problems of vibration for steplike loading is developed. The cases of suddenly applied stress which is maintained constant afterwards or changes sign steplike with the period of free vibration, are studied. Continuously distributed and localized friction are considered. It is shown that extension of a zone of disturbances and dissipation in a system with friction, stricly depends on the history of loading.
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