A finite element-based mode-matching technique for computation of the scattered wave fields from spatiotemporally modulated elastic media

Previous work by the authors provided the derivation and implementation of a finite element approach to model nonreciprocal elastic wave propagation for media in which the material properties are functions of both space and time [Goldsberry et al., J. Acoust. Soc. Am. 146(1) (2019)]. That work employs a harmonic balance approach to calculate propagating modes in a periodic medium. The present work adapts the aforementioned finite element approach to compute the scattered elastic wave field from finite structures having spatiotemporally modulated material properties. Calculation of the scattered field requires a domain truncation technique that accounts for the radiating modes at each generated harmonic of the modulation frequency. We derive and implement a mode-matching boundary condition using a Galerkin framework, which weakly enforces the continuity of the stresses and displacements at the boundary between the computational and the exterior analytical domain. We show that this approach is similar to a Dirichlet-to-Neumann boundary condition. Finally, we demonstrate this domain truncation technique as a means to compute the reflected and transmitted elastic wave fields from a proposed nonreciprocal elastic wave circulator design. [Work supported by NSF EFRI.]