Analysis of dynamic Green’s functions of discrete flexural systems

Abstract

This thesis investigates the dynamical behavior of Euler–Bernoulli beams in a 2D square lattice. Analytical solutions will be provided for the fourth-order Euler-Bernoulli PDE relating to boundary conditions which will be applied to the beams ends. The discrete Fourier transformation is used to generate explicitly dispersion curves, and their behaviors and properties are described. A numerical procedure for evaluating Green’s function that is based on the MATLAB software is presented. Furthermore, the Euler–Bernoulli beams problem in a 2D square lattice is developed to include the mass matrix of a central node, such that the amount of mass removed from the central junction. Thus, the purpose of this study is to investigate localizable defect modes caused by a line defect of a finite type. Mass defect Green’s function is obtained, and the system is then transformed into an eigenvalue structure. The phase diagram of a two-dimensional parameter diagram is achieved by establishing a reliable numerical evaluation of eigenvalue system.