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.