A Numerical Study of a Homogeneous Beam With a Tip Mass

Abstract

In this paper, we prove the existence and uniqueness of the weak solution of a flexible beam that is clamped at one end and free at the other; a mass is also attached to the free end of the beam. Also, we construct a finite element method, based on piecewise cubic Hermitian shape functions. Next, we derive error estimates for the semi-discrete Galerkin approximations. The results are derived from \cite{BS}. Finally, we implement the results of numerical schemes developed.