Efficient phononic band gap optimization in two-dimensional lattice structures using extended multiscale finite element method

The application of two-dimensional lattice structures is increasingly prevalent due to their significant potential in various multifunctional applications such as energy absorption, heat dissipation, and sound insulation. Similar to phononic crystals, lattice structures exhibit periodicity, and being composed of lightweight rods, they are sensitive to vibrations. Incorporating the concept of acoustic metamaterials into lattice structures can facilitate the design of lattices with vibration isolation properties. However, the low-frequency bandgaps generated by local resonances in lattice structures tend to be narrow. To widen the frequency range of these low-frequency bandgaps, several studies have emerged. This study focuses on rapidly optimizing the phononic bandgaps of two-dimensional lattice structures, aiming to efficiently and accurately determine the optimal geometry of each truss unit, thereby exhibiting outstanding vibration (elastic wave) isolation within a specific frequency range (bandgap). The proposed approach employs an Extended Multiscale Finite Element Method (EMsFEM) to achieve equivalence in the mechanical performance of truss structures, enabling the rapid computation of bandgap optimization for lattice structures with large-scale truss units. The results illustrate the effectiveness and feasibility of this method, which can attain broadband low-frequency bandgaps without compromising computational efficiency.