Time-Modulated Local Defect as a Mechanism for Controlled Frequency Conversion in a Finite Phononic Crystal

This work investigates the effect of a dynamically modulated defect on the propagation of mechanical waves in a quasi-one-dimensional phononic crystal. The studied structure consisted of periodically arranged meta-atoms with different cross-sectional areas, and a local defect enabled a periodic change in the geometry of one of the elements. The transmission characteristics of the static structures were determined using the transfer matrix method (TMM), while wave propagation in space and time was analyzed using the finite difference time-domain method (FDTD). Numerical results were experimentally verified using a four-microphone impedance tube. It was shown that changing the defect cross-sectional area allows for controlling the fundamental bandgap width and the positions of adjacent transmission maxima and minima. The introduction of periodic defect modulation led to modulation of the transmitted wave amplitude and the generation of additional spectral components with frequencies fs+kfp, related to the periodic time modulation. Increasing the modulation frequency and amplitude resulted in an increase in the observed effects and amplitudes of the generated frequency components. The conducted analysis showed that the dynamic defect can be used to control the transmission and conversion of frequencies in phononic structures.