Steady state propagation of a rectilinear crack in a thin elastic plate supported by a Winkler elastic foundation

We consider steady state propagation of a rectilinear crack in a infinite thin elastic Kirchhoff plate bilaterally supported by an elastic Winkler foundation. The crack flanks are subjected to a continuous (between the flanks) harmonic load. The problem's governing equation features the biharmonic operator together with a curvature (along the crack) term. Through application of the Fourier transforms to the even/odd part of the problem, a pair of inhomogenenous uncoupled Weiner-Hopf equations is met. Solution is obtained through numeric factorization of the kernel function. The full-field solution is given, together with conditions on the energy radiation. The special case of stationary crack is also retrieved.