Dispersion analysis of periodic structures by solving corresponding excitation problems

Dispersion analysis of periodic structures with complicated material distributions is conventionally performed by solving eigenproblems where a unit cell with periodic boundary conditions is appropriately discretized and an algebraic eigenproblem solver is applied to the resulting linear equation system. In this paper, the same discretization models are employed but the solution of an algebraic eigenproblem is avoided. In contrast, the equation system is solved for an appropriately designed excitation and the dispersion behaviour is obtained from the resonance behaviour of the solution. This solution procedure is often much more robust than algebraic eigenproblem solutions and provides for particular physical insight into the problems.