Analysis of Bandgap Formation Mechanism Based on the Programmable Curved-Beam Periodic Structure

In order to investigate the propagation and isolation mechanisms of elastic waves, we propose a programmable curved beam periodic structure (PCBPS). The PCBPS is assembled by a unit cell containing bistable curved beams, which is equivalent to a spring oscillator system, and is used to analyze the principle of bandgap formation. We employ the finite element method (FEM) and theoretical analysis to validate the proposed equivalent model. By equating the spring oscillator system, we compute closed-form solutions to demonstrate the accuracy and predictability of the dispersion relation. Our results show that the spring-oscillator model can accurately predict the structural bandgap of PCBPS while obtaining the effect of the geometrical parameters of the unit cell on the structural bandgap. The ideas presented and the results obtained have significant potential for designing functional structures and facilitating the practical application of periodic structures for wave insulation and propagation control in different frequency ranges.