Free Vibration of Beams via Finite Difference Scheme

Abstract

This paper aims to present the finite difference scheme tackling with the wave equation. Based on finite difference scheme, the dynamic equilibrium shapes and natural frequency of three types of beams (e.g. simple, fixed-fixed and cantilever beams) have been evaluated. For dynamic equilibrium. the explicit finite difference equations have been derived , the consistency of the scheme has been proved and the stability of the scheme has been determined. The natural frequencies are demonstrated by finding the lowest eigenvalue of each type of the beam. From the results, it is found that the accuracy of the results depend on the number of discretization for both time and space…