Nonreciprocal vibrations of finite elastic structures with spatiotemporally modulated material properties

Abstract

Elastic waveguides with time- and space-dependent material properties have received great attention as a means to realize nonreciprocal propagation of small-amplitude mechanical waves in unbounded elastic media. Previous works have shown that propagating waves in a modulated medium violate reciprocity by means of asymmetric frequency and wave number conversion between two counterpropagating modes. In the present study, we investigate nonreciprocal longitudinal and transverse vibrations in a finite elastic waveguide with time- and space-dependent material properties. A semianalytical approach based on coupled mode theory is derived, which makes use of the mode shapes of the nonmodulated beam subject to a set of imposed boundary conditions. The modulation parameter space is explored for designs that yield a large degree of nonreciprocity for low-frequency longitudinal and transverse vibrations. For the cases considered in this work, only a small subset of modulation parameters displays strong nonreciprocity, which reveals a sparse and complex design space that must be analyzed in order to create nonreciprocal wave devices.