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Size-dependent complex band structure of tunable beam metamaterial with shunted piezoelectric array

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Abstract

This study investigates the size effects on the dispersion relation of the transverse waves propagating through micro-beam metamaterial covered by piezoelectric patches that are connected with external shunted circuits. Based on the modified couple stress theory and Hamilton’s principle, the transfer matrix model is established for determining the complex band structure which incorporates the length scaling effect and the electromechanical resonance. Numerical results show the size-dependent behavior of the complex band structure in terms of the location, the range, and the decaying level. The differences are indicated between the results obtained by the non-classical model and the classical elasticity-based model and the effects of Poisson’s ratio. The connection modes of the piezoelectric layers on the characteristics of transverse wave propagation and attenuation are also examined. Further, the tunable nature is demonstrated via investigating the influences of the unit cell length, the circuit parameters, and the distribution of piezoelectric materials on the attenuation diagram.

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Acknowledgements

The present work was supported by the Natural Science Foundation of Hainan Province (No. 2019RC068) and the National Natural Science Foundation of China (No. 51909050).

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Authors and Affiliations

  1. Mechanical and Electrical Engineering College, Hainan University, Haikou, 570228, People’s Republic of China

    Jingru Li, Zhongjian Miao & Qingfen Ma

  2. Qingdao Innovation and Development Center, Harbin Engineering University, Harbin, 150001, People’s Republic of China

    Wei Lin

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Li, J., Miao, Z., Ma, Q. et al. Size-dependent complex band structure of tunable beam metamaterial with shunted piezoelectric array. Acta Mech 233, 889–904 (2022). https://doi.org/10.1007/s00707-022-03145-2

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