Green's function of a thin circular plate with elastically supported edge

The Green's function that is suitable for immediate computations, is obtained for a thin circular Poisson–Kirchhoff plate of a uniform thickness. The plate's edge is elastically supported so that the boundary values of the radial bending moment equal zero, while the shear force is directly proportional to the deflection function on the boundary. The extended version of the classical method of eigenfunction expansion is used with partial summation of the resultant Fourier expansion. The ‘singular’ component of the Green's function is analytically split off. This makes the representation accessible for engineering computations.