Space-time modulation provides a powerful approach for controlling wave behavior and enables forms of wave manipulation that are unattainable in stationary systems. Here, we propose a generalized transfer matrix method for analyzing wave propagation in periodic space-time modulated systems. The proposed method relaxes the commonly assumed sinusoidal modulation constraint and accommodates an arbitrary number of time-varying components with general periodic modulations. A two-membrane acoustic system subjected to three representative periodic modulations — namely, square-wave modulation, triangular-wave modulation, and sawtooth-wave modulation — is investigated. The results demonstrate that the proposed method enables accurate and efficient analysis of weakly modulated space-time periodic systems. This framework provides a versatile tool for analyzing complex space-time modulated structures and may facilitate the development of advanced acoustic devices for applications such as underwater communication, medical ultrasound, and noise control.
Zhu et al. (Thu,) studied this question.