Asymmetric elastic wave scattering in elastic plates

Reciprocity is a fundamental principle that can be used to understand a wide range of wave phenomena. In reciprocal systems, the exchange of source and receiver between two points yields the same displacement at the receiver if the applied force at the source is the same for both configurations. The reciprocity principle enforces restrictions on the scattering matrix in an acoustic or elastic system, but these relationships are not obvious when multiple modes are present, particularly when modes are coupled due to the presence of asymmetric scatterers. In this talk, we apply the reciprocity principle in a simplified two-dimensional waveguide case to prove symmetry of the scattering matrix in passive systems with and without loss and establish requirements for asymmetric scattering. The requirements enforced by reciprocity and energy conservation are then generalized to Lamb modes of arbitrary order. Applications to acoustic and elastic metamaterial design and ultrasonic nondestructive evaluation are discussed. [Sandia National Laboratories is a multimission laboratory managed and operated by National Technology and Engineering Solutions of Sandia, LLC., a wholly owned subsidiary of Honeywell International, Inc., for the U.S. Department of Energy’s National Nuclear Security Administration under contract DE-NA-0003525.]