Construction of the exact solution of the ring-plate problem by solving functional equations

摘要

This paper presents a method of constructing the exact solution of the ring-plate problem. The method is based on the general solution formula (nonseries form) of the biharmonic equation. The method changes solving the boundary-value problems of the ring plate into solving three functional equations and computing the coefficients of a simple Fourier series, or only solving four functional equations. The method is believed to be new. The simpler formulas of the solutions of all cases of the ring-plate boundary-value problems without any free boundary are obtained. Several examples are given.