Topological states in a one-dimensional stepped beam with resonators

Abstract

Topological metamaterials offer defect-immune edge or interface states for elastic wave control and play an important role in robust waveguiding. One-dimensional topological metamaterial beams with engineered features, such as grooves or resonators, can be tailored to support topological states, offering great potential for advanced mechanical applications. However, most existing works focus on a single type of feature, limiting the number or quality of achievable topological states, especially in terms of low-frequency localization and energy concentration. In this study, a one-dimensional stepped beam structure with resonators is proposed, employing a strategy that integrates both Bragg scattering and local resonance mechanisms to support multiple and highly concentrated topological interface states. First, the hybrid structure is constructed by introducing periodic grooves and attaching subwavelength resonators to the beam, enabling the coexistence of Bragg scattering and local resonance mechanisms. The topological properties of two traditional configurations in one-dimensional beam structures are studied for comparison. The concentration factor is introduced to quantitatively assess the energy localization of the topological states. Subsequently, the finite element simulations for the studied model are performed. The Zak phase calculations and the transmission results indicate the existence and the high localization of topological states. Finally, transmission experiments further confirm the existence and robustness of topological interface states. The results show that the proposed model supports two robust and strongly localized topological states, performing better than traditional designs in terms of energy concentration and structural adaptability. This work offers a practical and flexible strategy for low-frequency vibration control, which has potential for future development of elastic wave sensors and energy harvesting devices.

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