The Optimization Of Band Gap For 2D Phononic Crystals

Phononic crystals(Pn Cs)are periodic structural composites with elastic wave band gap,i.e.,the propagation of elastic waves is suppressed in the band gap frequency range,while in other frequency ranges elastic waves will propagate without loss,which makes it a promising application in vibration and noise reduction.In recent years,band gap modulation of Pn Cs has been a hot topic for researchers all over the world.The current literatures are limited to study the Pn Cs band gap optimization problems with fixed materials.However,it is shown that increasing the diversity of materials is good for obtaining the desired band gap characteristics.Therefore,it is important to carry out research on the optimization for the band gap of Pn Cs by selecting suitable materials from a variety of materials.In this thesis,the optimization of the band gap for 2D Pn Cs with material self-selection is carried out based on an evolutionary algorithm.The details of the study are as follows:First,a single-objective optimization(SOOP)study of the band gap of 2D Pn Cs based on genetic algorithm(GA)was carried out.The results show that in the case without pores,the band gap generation mechanism of the optimized structure changes from local resonance to Bragg scattering compared with the “seed” structure for the out-of-plane mode;and for the inplane mode,the number of material of the reduced from four to three for optimized structure,compared with the “seed” structure.In the case of pores,the introduced solid connected domain constraint can achieve the optimization of the target while ensuring the practical significance of the optimized configuration.Secondly,a multi-objective optimization(MOOP)problem for the band gap of 2D Pn Cs considering both band gap and mass requirements is investigated based on the non-dominated ranking genetic algorithm(NSGA-II).The results show that MOOP not only yield nondominated solution close to the approximate optimal solution of SOOP,but also yield other non-dominated solutions of MOOP problem.The decision makers can select the suitable solution from the solution set according to their needs.Finally,the problem of optimizing the band gap of 2D Pn Cs considering manufacturing constraints,i.e.,adding the connectivity requirement of the manufacturing material to the constraints,is investigated.The results show that the optimized Pn Cs configurations can satisfy the manufacturing requirements,which can provide basis for the application of Pn Cs.The research in this thesis provides a solution to the problem of selecting suitable materials from multiple materials for Pn Cs band gap optimization.