Classical solutions of forced vibration of rectangular plate driven by displacement boundary conditions

Forced vibration of a rectangular plate excited by displacement boundary conditions is investigated. The system of boundary conditions is decomposed into two fundamental types of sub-systems, which involves only one side or one corner. The necessary conditions for the solutions to be of classical sense are discussed. The transformation is designed to convert the problems to those of forced vibration by body forces with homogeneous boundary conditions. The closed-form solutions are derived for these two types of problems, using Fourier series. Additional conditions are proposed to the boundary functions so that the differentiated series converges uniformly. And consequently, the solutions are verified to satisfy the differential equations in a classical sense with continuous derivatives.