Abstract
A nonlinear viscoelastic material whose constitutive functional is represented by a multiple integral expansion, with the characteristic property that the instantaneous response is linear, is called semilinear. It is shown that, in a longitudinal impact on the end of a long bar of such a material, the velocity (or stress) is governed by a nonlinear integro-differential equation. If the velocity (or stress) is prescribed at the end of the bar, then the solution may be obtained in the form of a traveling wave, with the state variables behind the wave front expressed in the form of power series whose coefficients are obtainable by quadratures. A sample calculation exhibits the quantitative effects of nonlinear memory on wave propagation. The method used in the paper is also shown to be extendable to certain problems of three-dimensional wave propagation.
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