Tunable topological interface states via a parametric system in composite lattices with/without symmetric elements

doi:10.1007/s10483-024-3194-9

摘要/Abstract

Abstract:

Over the past decades, topological interface states have attracted significant attention in classical wave systems. Generally, research on the topological interface states of elastic waves is conducted in the lattices with symmetric elements. This paper proposes composite lattices with/without symmetric elements, and demonstrates the realization of tunable topological interface states of elastic waves via parametric systems. To quantize the topological characteristics of the bands, a modified Zak phase is defined to calculate the topological invariant by the eigenstates for the lattices with/without symmetric elements. The numerical results show that the tunable frequencies of topological interface states can be realized in composite lattices with/without symmetric elements through the modulation of the parametric excitation frequency. The tunable topological interface states can be introduced into the vibration energy harvesting to design efficient and steady energy harvesting systems.

Key words: metamaterial, topological interface state, parametric excitation, asymmetric element, modified Zak phase

中图分类号:

37C80

. [J]. Applied Mathematics and Mechanics (English Edition), 2024, 45(12): 2055-2074.

Jianguo CUI, Tianzhi YANG, Wenju HAN, Liang LI, Muqing NIU, Liqun CHEN. Tunable topological interface states via a parametric system in composite lattices with/without symmetric elements[J]. Applied Mathematics and Mechanics (English Edition), 2024, 45(12): 2055-2074.

图/表 15

参考文献 49

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Parametric excitation frequency	0	10	20	30
Cases 1 and 2	1.414	1.581	2.000	2.550
Case 3	1.366	1.548	1.984	2.542
Case 4	1.577	1.738	2.138	2.665

Boundary type	$ \alpha_1 >\alpha_2 $	$ \alpha_1 <\alpha_2 $
Lower boundary	$ \pi $	0
Upper boundary	0	$ \pi $

Boundary type	$ \mu_1 >\mu_2 $	$ \mu_1 <\mu_2 $
Lower boundary	0 or $ \pi $	$ \pi $ or 0
Upper boundary	$ \pi $ or 0	0 or $ \pi $

Mass relationship	Boundary type	$ \alpha_1 >\alpha_2 $	$ \alpha_1 <\alpha_2 $
$ \mu_1 >\mu_2 $	Lower boundary	$ \pi $	0
$ \mu_1 >\mu_2 $	Upper boundary	0	$ \pi $
$ \mu_1 <\mu_2 $	Lower boundary	$ \pi $	0
$ \mu_1 <\mu_2 $	Upper boundary	0	$ \pi $