Semi-Analytical Solutions for Wave Propagation of Periodically Repetitive Schwarz Primitive Triply Periodic Minimal Surface Based Structure Embedded With Acoustic Black Hole Resonators

Abstract

The Schwarz Primitive triply periodic minimal surface (P-TPMS) lattice structure is attracting more attention due to its superior mechanical properties and unique topological configuration. In this study, a new periodic configuration is proposed in which the unit cell is formed by embedding the acoustic black hole (ABH) component in the primary P-TPMS component. A semi-analytical method is developed to calculate the wave propagation properties of the proposed structure. The dynamical equilibriums of the primary P-TPMS and ABH components are described by the finite element method and the WKB method respectively. By considering the compatibility at the connections between the components and using the equivalent dynamic stiffness technique, dispersion analysis can be implemented in the framework of the wave and finite element (WFE) method. Various numerical examples with different number, type and connection position of the resonators are investigated. By comparing the calculation results from the present semi-analytical method with that from the finite element method, the effectiveness of the proposed method is validated. The influences of the number, type, and connection position of the resonators on the bandgap properties are investigated.

Elastic wave control in reticulated plates using Schwarz primitive cells

“…Static properties of the Schwarz primitive cell are well known, and research is ongoing to design porous and bone mimicking scaffolds based on such geometries for medical applications and bone implants. From a dynamic point of view, the performance of structures based on the Schwarz primitive cell for vibration and elastic wave guiding has been previously investigated [26,28]. However, studies on the capacity of such structures in regard to wave mitigation and focusing in the context of metamaterials are missing.…”

“…This minimizes stress concentrations, improving stress distribution and eventually making the frame less prone to fatigue damages [24,25]. The Schwarz primitive cell has previously been investigated for its buckling characteristics [26], numerically and experimentally validated for topological elastic wave guiding [27], and has also been explored for vibration mitigation purposes in the realm of acoustic black holes [28]. An in-depth investigation on the relationship between the volume ratio and bandgap behaviour [29], as well as the acoustic properties of Schwarz primitive cell [30] and mechanical vibration bandgaps [31], have been performed.…”