A numerical study on longitudinal vibration for fixed free bar using finite difference method and discretization technique

Abstract

This paper aims to determine the variation of the axial displacement in a fixed bar using Finite Difference Method (FDM). The mathematical modeling is derived based on the wave equation and solved by analytically using method of separating variables involving second derivative of axial displacement, , and the corresponding of the second derivative of finite difference. The algorithm for Finite Discretization Method analysis is done using FORTAN and the result is plotted using MATLAB. The result shows that the deflection of the bar is proportional due to the changes of the time.