Abstract
We consider a nonlocal (peridynamic) version of the classical forced wave equation. This scalar three-dimensional equation contains a weight function (the “micromodulus”) and a length parameter (the “horizon”) that have to be selected. We investigate various properties (the locality limit as the horizon shrinks, plane waves and group velocity), paying attention to how these properties depend on the choice of the micromodulus. We solve the forced peridynamic equation in the static case (avoiding divergent integrals) and in the time-harmonic case (with a radiation condition, when needed).
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