The interpolation solution of the second basic plane problem of the dynamics of elastic solids

The second basic plane problem of the dynamics of elastic bodies is considered in the Muskhelishvili formulation, when the known boundary displacements are replaced by interpolation time polynomials and the known initial conditions are replaced by polyharmonic functions, which interpolate the initial conditions in a region with a finite number of interpolation nodes. In this case a solution of the problem, called here the interpolation solution, is possible. It must satisfy the dynamic equations and interpolate the boundary displacements and initial displacements and velocities. This solution is constructed in the form of a polynomial and is reduced to solving a series of boundary-value problems for determining the coefficients of this polynomial.