1-D Wave Propagation

The 1-D stress wave propagation problem is simulated with a 2D geometry. The problem geometry is shown below on the left hand side. Theoretical solution can be derived for this problem.

The figure below shows how the velocity solution, from simulation (black and blue), plotted with time at the middle of the bar compares with the theoretical solution (red). The black curve is obtained when coarser nodal spacing is used while blue corresponds to that with a finer spacing.

Click the image below to see an animation of the velocity wave propagating towards the rigid end and reflecting back.