ABSTRACT
This chapter considers a different kind of time-dependent problem which involves second-order time derivatives in the finite element equations. When a time-dependent force caused by factors such as an impact, blast, and earthquake loading impinges on a medium, it is transmitted through the medium as a stress wave. Generally such waves propagate in all the three spatial directions. Under certain circumstances and assumptions, it is possible to idealize the medium as one-dimensional. Time-dependent force acting on the bar causes vibrations in the bar, and a stress wave propagates to and fro in the bar. Then governing differential equation for the one-dimensional case is often known as the wave equation. The element equations can now be added such that interelement continuity of displacements and accelerations are ensured at common nodes. The consistent mass formulation shows oscillations and inaccuracies, particularly in the vicinity of the wave front.
