Structural differences in wave propagation in discrete and continuous systems

Summary

The harmonic and transient behaviours of one-dimensional discrete semi-infinite cascades of masses and springs have been derived from analytical pulse response solutions [1]. The investigation shows structural differences between the dynamic behaviour of models with distributions of mass over the “finite” elements as compared to continuous models. Two generally accepted ideas are scrutinized. Firstly, that the dynamic behaviour of a discrete model after a refinement of the mesh converges to the response of the underlying continuous model. Secondly, that a symmetric mass distribution over the element results in a better convergence. Both ideas need some adjustment.