Topological Valley Transport of Plane Elastic Wave in a Hexagonal Lattice with Tapered Beams

Introduction: This study examines the impact of 26-week exercise intervention facilitated by IoT devices on cognitive function, hippocampal volume, and health indicators in a real-world setting based on the Transtheoretical Model. Aim: The purpose of this study is to investigate the topological elastic waveguides exploiting the hexagonal lattices with tapered beams. Article structure: We numerically demonstrate topologically protected edge modes of in-plane motion and their propagation in a hexagonal lattice with tapered beams. The frequency range of topologically protected edge modes is investigated and analyzed in detail according to the taper factor of the tapered beam that controls the spatial symmetry. The rest of this article is as follows. In Section 2, the structural design and band structure of a hexagonal lattice with tapered beams are presented and analyzed. Section 3 analyzes the topological phase transition in the band structure and the effects of the taper factor and material parameters on the band gaps. Section 4 confirms the topologically protected interface states of a hexagonal lattice supercell with tapered beams, which are attributed to designing three different elastic wave propagation routes and demonstrate the transmission performance in the time and frequency domains. In addition, the effect of local defects on waveguide transmission is also compared. Last, the conclusion is summed in Section 5. Method: The main methods used in this study are finite element method, Bloch theorem and structural dynamics simulation technology. Conclusions: In this paper, topologically protected elastic waveguides using a hexagonal lattice with tapered beams are achieved to guide plane elastic waves. The customizable nature of valley-related edge modes relating to the taper factor and slenderness ratio is demonstrated numerically. The taper factor can be adjusted to break the spatial inversion symmetry, resulting in the valley edge state and interface state. The application of hexagonal lattices with tapered beams can effectively guide elastic waves, which provides a simple method to tailor topologically protected edge modes and mechanical properties for various structural applications in sound and vibration control.