Completeness Of Eigenfunction Systems For The Products Of Two Operator Matrices And Its Application In Elasticity

The completeness theorem of the eigenfunction systems for the product of two2×2symmetric operator matrices is proved. The result is applied to4x4off-diagonal infinite-dimensional Hamiltonian operators. A modified method of separation of variables is proposed for separable Hamiltonian system. As an application of the theorem, the general solutions for the plate bending equation and the free vibration of rectangular thin plates are obtained to show the correctness of the results.Plate and shell mechanics are very important fields in the study of elasticity. Mindlin plate bending problems is derived to separable Hamiltonian system by choosing proper dual vectors. Applying the structural characteristics of off-diagonal Hamiltonian operator, a complete biorthogonal expansion of Mindlin plate bending problems with two opposite sites simply supported is established through the products of operator matrices. The exact solutions of deflections and bending moments for the Mindlin plate bending problems with two opposite sites simply supported are obtained.The main theoretical results with the actual mechanics examples to verify the accu-racy and validity of the method is a feature of the dissertation.