Free Vibration Problems Of Rectangular Thin Plates On Two-parameters Elastic Foundation By The Hamiltonian Method

In this thesis,the free vibration equations of rectangular thin plates are transformed into Hamiltonian system using pseudo-division algorithm for matrix multi-variable poly-nomial.And Hamiltonian operators are obtained by means of separation of variables method.By calculating,the eigenvalues and eigenvectors of the Hamiltonian operators for the problem with two opposites simply supported are derived.Then,the symplectic orthogonality and the completeness of the eigenvectors(in the sense of Cauchy.s principal value)are proved.Based on the completeness of the eigenvectors,the general solutions of the Hamiltonian systems are obtained and the general solutions of rectangular thin plates on two-parameters elastic foundation with two opposites simply supported can be obtained.Then,we use two examples to illustrate that the frequency and deflection of the free vibration problems are directly solved by the present method.Furthermore,the Hamiltonian method also studies the free vibration problems of orthotropic rectangular thin plates on two-parameters elastic foundation and the result are verified through two examples.