Contribution
Chiral symmetries for guided wave computations
* Presenting author
Abstract:
Symmetries play an important role in physics and engineering, as they allow to drastically simplify many problems. However, the exact procedure that achieves this simplification can be tricky to find. In the first part of my talk, I give a short, educational introduction into the exciting topic of symmetries and discuss some general strategies of using them. In the second part, I will demonstrate how symmetries can be used in calculating the dispersion relation of guided elastodynamic waves in plates. In the case that we consider, the dispersion relation is invariant under changing the sign of the wave vector $mathbf{k}$. This invariance is the consequence of a so-called chiral symmetry of the underlying quadratic eigenvalue problem. We exploit this symmetry to decompose the problem into two other eigenvalue problems of half the size of the original one. As the used numerical procedure to compute eigenvalues increases cubically with the matrix size, this leads to a speedup of approximately factor eight.