Nonreciprocal vibration transmission using dislocated displacement feedback

This paper examines absolute displacement feedback using dislocated sensor-actuator pairs to design and implement an active metamaterial cell for nonreciprocal vibration transmission. Comprehensive stability and performance analyses are carried out, both theoretically and experimentally. The theoretical analysis yields a simple condition on parameters of the example two-degree-of-freedom metamaterial cell to guarantee the stability. If the condition is respected, very large feedback gains can be implemented so that the difference in vibration transmission in the two opposite directions may be substantial. This is confirmed experimentally: the nonreciprocity measured in terms of the amplitudes of two characteristic transfer mobilities of the cell amounts to about 30 dB in the frequency range between 30 and 1000 Hz. As shown in the Appendix to the paper, the cell could be used as a prefabricated and pre-tuned modular building block to form a functional active metamaterial for nonreciprocal vibration transmission.