Abstract
The Euler-Bernoulli beam theory is a simplification of the linear theory of elasticity which provides a means of calculating the load-carrying and deflection characteristics of beams. The beam equation,

EI ∂4u = −p∂2u describes the relationship between the beam’s deflection, u(x, t) and the applied ∂x4 ∂t2
load, p(x, t). This equation is widely used in engineering practices. When designing bridges and buildings, the engineers are interested in determining deflections because the beam may be in direct contact with a brittle material such as glass. Although analytical solutions to Partial Differential Equations (PDEs) are exact, they may not be easy to solve and in most cases, the solutions are in closed form. This makes numerical solutions ideal for such calculations. From the existing literature, the discussion on the beam equation is not exhaustive. It is therefore the aim of the study to investigate the numerical solution of the equation of structural analysis of a beam that incorporates the longitudinal movement. This study has managed to solve numerically the 4th order 2-dimensional beam equation, utt(x, y, t) + α2[uxxxx(x, y, t) + uyyyy(x, y, t)] = f (x, y, t) using the finite difference method subject to special boundary and initial conditions. The study has checked the accuracy of the numerical scheme by analyzing its stability and convergence. The results of this study indicate that the new algorithm has small computational work, faster convergence speed and high precision.
Keywords:- Euler-Bernoulli Beam Equation, Centered Time Centered Space, Finite Difference Representation, Courant Fredrichs Lewy Condition, Computational Domain.