Recent research in wave propagation and vibration behavior in materials with spatiotemporal modulation of bulk properties or boundary conditions has gained interest in order to control both the wavenumber and frequency characteristics of waves. In this work, a coupled mode theory is derived for acoustic systems for which the bulk properties or boundary conditions are modulated as a function of space and time. The approach expresses the dynamics of the modulated system as a function of coupled modes of the unmodulated system, which are determined using with standard analytical or numerical techniques. The spatiotemporal modulation of material properties or boundary impedances gives rise to coupling between the set of modes with unique shapes and differing discrete frequencies. The modulation therefore enables control over the spatial and temporal response of an acoustic system, including resonances, that cannot be achieved with unmodulated systems. A perturbation approach is then used to investigate the effects of mode coupling near modal resonances. We apply the theory for illustrative cases to demonstrate the use of spatiotemporal modulation to couple modes, with applications focused on propagating to evanescent mode conversion and resonance control. Work supported by ONR.
Goldsberry et al. (Wed,) studied this question.