Hamiltonian System and Viscoelastic Boundary Conditions

Abstract

Abstract By using Laplace integral transformation, the viscoelastic stress-strain relationship in the time domain is described as an algebraic equation in Laplace space, which makes the Hamiltonian system method smoothly implemented. Thus, the basic control equations with displacement and stress as basic variables are established, and the viscoelastic problem is transformed into the eigenvalue and eigensolutions. The eigensolutions include a series of independent functions, in which the zero eigenvalue eigensolutions cover all the basic deformations such as tension and bending, and do not decay with the space coordinates.