Symplectic Superposition Solution Of A Free Orthotropic Rectangular Thin Plate On An Elastic Foundation

The Hamiltonian canonical equations of the bending equation of an orthotropic rectangular thin plate resting on an elastic foundation are studied,and the eigenvalues and eigenfunctions of the Hamiltonian operator for the plate problem with two opposite edges slidingly supported is calculated.It is proved that the eigenfunctions are symplectic orthogonal and complete in the sense of Cauchy's principal value.And based on the completeness of the eigenfunctions,the general solution of the orthotropic rectangular thin plate resting on an elastic foundation with two opposite edges slidingly supported is presented.Then the analytical bending solution of the fully free orthotropic rectangular thin plate resting on an elastic foundations is derived by using the symplectic superposition method.Finally,the validity of the obtained analytical solution is proved by two specific examples.