Dispersion engineering in 2D non-local mechanical lattices

Abstract By manipulating dispersion, planar lattices can be endowed with a variety of intriguing wave propagation characteristics, which hold significant value in controlling vibration energy transfer paths, energy harvesting, noise suppression, and structural optimization design. In the realm of twisted moiré physics, dispersion modulation from elliptical to hyperbolic can be achieved through bilayer twisting; however, such designs pose certain challenges for mechanical structures. This paper proposes a two-dimensional topological mechanical phononic crystal model based on nonlocal dispersion engineering. By designing a spring-mass lattice structure with adjacent and nonlocal couplings, the propagation modes of mechanical waves are effectively controlled. Through flexible and straightforward design of nonlocal connection methods, structures with specific dispersion properties can be easily constructed. The paper also discusses the influence of nonlocal connection methods and stiffness parameters on dispersion. This research provides new insights for designing acoustic metasurfaces and mechanical structures with tailored wave propagation properties, offering broad application prospects, such as directional energy harvesting and intelligent vibration isolation systems.