On the Analytical Solutions of Two Singular Integral Equations with Hilbert Kernels

Abstract

The analytical solution of two singular integral equations with Hilbert kernel of the first and second kind, respectively, is derived from the known solution of the corresponding singular integral equations with Cauchy kernel of the first and second kind by introducing a proper change of variables.

Solid circular plate unilaterally supported along two antipodal edge arcs and deflected by a central transverse concentrated force

“…Protracted attention has been paid by the researchers to the mechanical analysis of circular plates subjected to nonaxisymmetric boundary conditions. The first study on this kind of problems has been carried out by Sherman, 1,2 whereas more recent contributions are those by Strozzi and Vaccari, 3 Monegato and Strozzi, 4,5 and Strozzi and Monegato, 6 in which the contact problem is described in terms of Hilbert–Prandtl singular integral equations, 7 formulated in terms of the exact expression of the influence function for thin circular plates. 8 The title study addresses a different kind of problem, i.e.…”