Abstract
We have theoretically investigated the properties of the stress wave propagation which is caused by a longitudinal impact of a cylindrical bar by a one-dimensional model. In the present study, the effects of the boundary condition and material nonlinearity of the bar are taken into account. An exponential function is chosen as the constitutive equation in order to realize that the one-dimensional model possesses some useful properties for the analysis. A governing equation which describes the behaviors of the stress wave is derived from the one-dimensional model. Since the governing equation is complicated, some mathematical techniques are applied in order to analyze the behaviors of the stress wave. As a result, it is shown that the stress wave, which can propagate through the cylindrical bar of semi-infinite length and that of finite length, is derived exactly from the governing equation. Moreover, the behaviors of the stress wave are shown analytically.
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