TY - JOUR

T1 - Non-Hermitian skin effect in a phononic beam based on piezoelectric feedback control

AU - Jin, Yabin

AU - Zhong, Wenxin

AU - Cai, Runcheng

AU - Zhuang, Xiaoying

AU - Pennec, Yan

AU - Djafari-Rouhani, Bahram

N1 - Funding Information: This work was supported by the National Natural Science Foundation of China (No. 11902223), the Young Elite Scientists Sponsorship Program by CAST (No. 2021QNRC001), the Shanghai Science and Technology Committee (Grant No. 21JC1405600), the program for professor of special appointment (Eastern Scholar) at Shanghai Institutions of Higher Learning, and the Fundamental Research Funds for the Central Universities.

PY - 2022/7/11

Y1 - 2022/7/11

N2 - Non-Hermitian systems have gained a great deal of interest in various wave problems due their ability of exhibiting unprecedented phenomena such as invisibility, cloaking, enhanced sensing, or the skin effect. The latter manifests itself by the localization of all bulk modes in a specific frequency range at a given boundary, with an unconventional bulk-boundary correspondence. In this work, we propose to realize the skin effect for flexural waves in a non-Hermitian piezoelectric phononic beam with feedback control between a sensor and an actuator in each unit cell. By implementing a non-Hermitian parameter, effective gain and loss can be achieved in the phononic beam characterized by complex eigen frequencies, and non-reciprocal pass bands are obtained. We highlight that the split point separating the gain and loss areas can occur not only at the edges of the Brillouin zones but also inside the same Brillouin zone. We further analyze the influence of the geometric and non-Hermitian parameters on the complex dispersions and the split point. The topology of the complex bands is characterized by the winding number, which supports the skin effect together with the non-reciprocity. The localization degree of the skin mode manifested by the enhanced beam's vibration energy at one boundary is related to the strength of the non-reciprocity, and the skin mode can be always excited regardless of the source position. Our results provide a potential platform to introduce non-Hermiticity into phononic or metamaterial systems with novel functions for elastic waves such as topological insulators, vibration attenuation or amplification, and energy harvesting.

AB - Non-Hermitian systems have gained a great deal of interest in various wave problems due their ability of exhibiting unprecedented phenomena such as invisibility, cloaking, enhanced sensing, or the skin effect. The latter manifests itself by the localization of all bulk modes in a specific frequency range at a given boundary, with an unconventional bulk-boundary correspondence. In this work, we propose to realize the skin effect for flexural waves in a non-Hermitian piezoelectric phononic beam with feedback control between a sensor and an actuator in each unit cell. By implementing a non-Hermitian parameter, effective gain and loss can be achieved in the phononic beam characterized by complex eigen frequencies, and non-reciprocal pass bands are obtained. We highlight that the split point separating the gain and loss areas can occur not only at the edges of the Brillouin zones but also inside the same Brillouin zone. We further analyze the influence of the geometric and non-Hermitian parameters on the complex dispersions and the split point. The topology of the complex bands is characterized by the winding number, which supports the skin effect together with the non-reciprocity. The localization degree of the skin mode manifested by the enhanced beam's vibration energy at one boundary is related to the strength of the non-reciprocity, and the skin mode can be always excited regardless of the source position. Our results provide a potential platform to introduce non-Hermiticity into phononic or metamaterial systems with novel functions for elastic waves such as topological insulators, vibration attenuation or amplification, and energy harvesting.

UR - http://www.scopus.com/inward/record.url?scp=85135096364&partnerID=8YFLogxK

U2 - 10.1063/5.0097530

DO - 10.1063/5.0097530

M3 - Article

AN - SCOPUS:85135096364

VL - 121

JO - Applied physics letters

JF - Applied physics letters

SN - 0003-6951

IS - 2

M1 - 022202

ER -