| As a new kind of man-made structure with spatial periodicity and forbidden characteristics for elastic/electromagnetic waves,phononic/photonic crystals have received wide attention of scholars at home and broad.Based on the characteristics of “small size controlling large wavelength” and energy localization,the locally resonant phononic crystals have an attractive application perspective within the field of low-frequency vibration reduction.Therefore,the study of this paper is based on the locally resonant phononic crystals with low-frequency damping characteristics to do research,for the purpose of obtaining the artificial structure of phononic crystal with the wide band gaps in low-frequency range and good damping property.Furthermore,for the problem of acousto-optic control,an optimal phoxonic crystal structure with dual band bands is proposed.With consideration of the problem of low frequency vibration,three local resonant phononic crystal structures are proposed in this paper: the windmill-like structure,the double panel structure,and the ring-like structure.Using the finite element analysis software COMSOL,the numerical simulation models of the three structures are established,respectively,and the frequency band structures and the vibration modes of the edges of the phononic band gaps are calculated.And the generation mechanisms of low-frequency band gaps for the three phononic crystal structures are revealed.Then,the influence of the sensitive geometric parameters of the three phononic crystal structures on the band gaps is studied to provide the basis and foundation for the optimization of phononic crystal structures.Finally,in order to verify the the effectiveness of the phononic crystal,the ring-like phononic crystal structure is selected as an example to carry out physical experiments.In order to meet the needs of low-frequency vibration suppression,it is necessary to obtain as large a band gaps as possible in the low-frequency range.Based on this,an optimization scheme with band gaps based on response surface method is proposed.Firstly,based on the sensitive structural parameters of phononic crystal structures,the numerical experiment scheme with three factors and seven levels is designed,and the functional relationship between structural parameters and band gaps is fitted by the response surface method.Secondly,the optimal band gaps and the corresponding geometric parameters are obtained by optimization model.Also,the optimal forbidden bands of the optimized windmill-like structure,double panel structure,and ring-like structure is within: [87Hz,125Hz] and [166Hz,247.8Hz],[93.3Hz,140.6Hz] and [153.4Hz,252.3Hz],and [69.5Hz,129.1Hz] and[143.9Hz,248Hz],respectively.For the problem of acousto-optic control,a novel phoxonic crystal structure is proposed in this paper,and the dual band gaps generation mechanism of the phononic and photonic band gaps is studied.And the influences of structural parameters of phoxonic crystal on the dual forbidden characteristics are explored.Then,the optimization scheme with band gaps based on response surface method is extend to the design of dual band gaps and the functional relationships between the dual band gaps bandwidth and structural parameters of phoxonic crystal structure are obtained.Finally,the unified objective function method is employed to establish a single objective optimization model,the optimal dual band gaps can be solved as: [0.4303,0.8117] and [0.379,0.4221],and corresponding optimal geometric parameters of phoxonic crystal structure can be determined as: f=0.0276 a,b=0.255 a,and d=0.255 a.The above research provides a feasible optimization scheme for the structure optimization of phononic/photonic crystals and the research of acoustic or optical metamaterials.In addition,the specific structures proposed in this pape provide alternative artificial functional materials for the vibration suppression in the low-frequency range and the acousto-optic control. |
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