The Complete Biorthogonal Expansion Theorem and Its Application to a Class of Rectangular Plate Equations

In this paper, we first establish the separable Hamiltonian system of rectangular cantilever thin plate bending problems by choosing proper dual vectors. Then using the characteristics of off-diagonal infinite-dimensional Hamiltonian operator matrix, we derive the biorthogonal relationships of the eigenfunction systems and based on it we further obtain the complete biorthogonal expansion theorem. Finally, applying this theorem we obtain the general solutions of rectangular cantilever thin plate bending problems with two opposite edges slidingly supported.