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Using the Sobolev-Smirnov method, we have found the exact analytical solution of a lon-gitudinal impact of semi-infinite plane elastic bars for any time after the impact. After collision, there are loading waves from contact surfaces of bars and unloading waves from lateral surfaces. Then the unloading waves reach the opposite surface of the bars and create the reflected loading waves. These loading waves reach the other surface of the bars and generate new unloading waves. The number of waves grows exponentially. The sum of waves tends to the wave of the one-dimensional approximation. [ABSTRACT FROM AUTHOR]

Using the Sobolev-Smirnov method we find the exact analytical solution of the longitudinal impact of semi-infinite plane elastic bars. The solution allows us to investigate wave propagations shortly after the impact. The obtained results allow us to compare the exact and approximate solutions of impact problems. We show that approximate solutions are wrong in a short time. According to the exact solution five waves are created in the first time after impact: one longitudinal loading wave and two unloading longitudinal waves from the lateral suifaces of the bars and two unloading transverse waves, also from the surfaces. We find singular points of the solution. It can be used for other applications such as any impact of two elastic bodies since the same waves arise and the same singular points exist at the impact. One of the singular points moves along suifaces with the speed of Rayleigh waves. At this point the bar suiface is perpendicular to the axis of the bars. Such a point arises at any impact. As the earth surface is also perpendicular to the direction of propagation of seismic waves, Rayleigh waves are especially destructive at earthquakes. [ABSTRACT FROM AUTHOR]