Time-space modulated structures (or dynamic structures) possess properties modulated both in time and space. They have been extensively studied in diverse areas. This presented work theoretically studies the unusual wave propagation phenomena induced by elastic waves incident on time-space modulated beams. The scattering matrix is developed to predict the characteristics of the reflected and transmitted waves. It is shown that the scattering matrix directly indicates the non-reciprocal wave transmission and frequency splitting phenomena caused by the dynamic beam, it also reveals a frequency conversion phenomenon, which is rarely noticed by researchers but has very significant influence on the application of dynamic structures.

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