Target-oriented inverse optimization design of phononic crystals with variable constraints for vibration attenuation

Abstract

Previous research on phononic crystals (PnCs) design mostly focused on the maximum band gap (BG) between adjacent orders and could not optimize the desired target frequency based on actual engineering problems. In order to achieve an arbitrarily specified BG structure of PnCs near the target frequency, a new topology design method for PnCs is proposed using a special triangular lattice PnC as the object. In the genetic algorithm (GA) optimization framework, two variable constraint optimization strategies, fixed-step and adaptive, are proposed to form a variable constraint genetic algorithm (VC-GA), which enables the non gradient optimization process to be continuous and uninterrupted. This optimization model also divides optimization into two stages, which can search for target individuals and maximize BG under the constraints of the target BG. Combining the optimization model with the improved fast plane wave expansion method (IFPWEM) for optimizing the single and multi-objective BGs in the in-plane and out-of-plane modes, and the weight coefficient is introduced to broaden its scope of application. The effectiveness of the method is verified through experiments, and the vibration reduction optimization design is carried out within a specific frequency range for the engineering structure corrugated plate as an example.