Response of a thin long nonhomogeneous elastic rod subjected to a time-dependent velocity impact is studied by the use of similarity transformations. Similarity representation of the original equation of motion and the associated conditions has been obtained in the form of an ordinary differential equation with variable coefficients and the corresponding boundary conditions. A general solution of the similarity representation is obtained in the form of series. Relations between the parameters of the problem for which the results hold have been obtained in the form of inequalities. The displacement and stress distribution in the rod is obtained for the admissible values of the parameters of the problem and the results are plotted for some of their discrete values. It is found that the stress is discontinuous at the wave front only in the special case of a homogeneous rod subjected to constant velocity impact; in all other cases the stress is found to be continuous at the wave front.
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