Numerical And Experimental Studies On Phononic Crystals With Criss-Crossed Elliptical Holes

Phononic crystals(PCs)are a kind of periodic composite materials with acoustic/elastic wave band gap characteristics.Among them,the porous PCs have always been a hotspot of research.Combining the porous PCs with soft materials gives rise to the soft PCs,whose band gaps can be effectively tuned by externally applied loads.As one of the most favorable topologies,two-dimensional(2D)soft PCs with squared circular holes have been extensively studied,the distribution of band gaps of which can be well tuned through post-buckling deformation under compression.However,there are some obvious shortcomings in the structure with circular holes;these include 1)geometric imperfections should be introduced to induce the corresponding post-buckling deformation,and 2)the tunability of band gap is generally poor at low porosity.Therefore,based on the contrarian thinking,we design a new porous structure with "criss-crossed elliptical holes",which is close to the post-buckling configuration of soft structures with circular holes.By combining the new configuration with both hard and soft materials,we study the characteristics and tunability of band gaps by means of both experiments and finite element(FE)simulations.The main contents and conclusion include:1.Based on the post-buckling configuration of 2D soft structures with circular holes,a new structure with criss-crossed elliptical holes is designed.Then thin hard PC plates(made of PMMA in this paper)with elliptical holes arrayed in a criss-crossed pattern are studied by experiments and FE simulations.The results show that the width of the band gap in the FX direction increases with the major-to-minor half-axis ratio of the elliptical hole as well as with the porosity of the structure.Compared with the PC with circular ones,the new structure is endowed with a wider low-frequency band gap.In addition,the propagation characteristics of elastic waves in the new structure can be changed by the introduction of different types of line defects,which actually leads to the reversely tunable function of the band gap.2.When combined with soft materials,the 2D periodic structure with criss-crossed elliptical holes can be easily deformed under mechanical loads.The deformation,band gap characteristics,band gap mechanism and tunable effects of stretching of this type of soft PCs are studied also using experiments and FE simulations.The results show that the width of the main band gap also increases with the major-to-minor half-axis ratio of the elliptical hole and the porosity of the structure.It is worth pointing out that,the change of the lower band gap boundary is the main factor affecting the frequency range of the main band gap,and it is closely related to the local resonance of the mass-and-ligament block unit.In addition,the uniaxial or biaxial tensile loading is applied to elongate the structure,which makes the initial band gaps become gradually narrow or even disappear.It is found that the equi-biaxial tensile loading has a better tunability on the band gaps.3.A loadable platform for wave propagation test is designed to study experimentally the tunability of band gaps of 2D soft PCs with criss-crossed elliptical holes via uniaxial stretching.The results verify the correctness and accuracy of the FE simulations,and further prove that uniaxial stretching can effectively control the band gap,making its width change from wide to narrow.4.With the self-designed uniaxial stretching device,the static deformation of the soft PC with criss-crossed elliptical holes is also studied experimentally.A"mass-ligament" model is used to analyze the variation of the effective Poisson's ratio of the structure with the uniaxial tension,in addition to the FE simulations.The results show that,with the increase of the uniaxial tensile load,the effective Poisson's ratio of the structure increases sharply at first and then grows smoothly,eventually reaching a certain value.It is further proved that,the structure undergoes two main deformation stages after being subjected to the uniaxial tensile load:the rotation of the mass and the stretching of the overall structure.In addition,the major-to-minor half-axis ratio of the elliptical hole and the porosity of the structure are all inversely proportional to the effective Poisson's ratio.Finally,a simplifying theoretical model is established,to briefly analyze the influence of uniaxial stretching on the rotation of the mass.In a word,the results of this thesis show that,compared with the traditional PC structure with squared circular holes,the one with criss-crossed elliptical holes has certain advantages,including richer initial band gaps,tunability of band gaps at a low porosity,and the robustness when the band gaps are tuned via deformation.Moreover,by applying different kinds of tensile loads to the 2D soft PC with criss-crossed elliptical holes,the band gap distribution(in terms of number,width,and lower and upper boundary frequencies)can be flexibly controlled to meet special requirements of practical engineering applications,such as vibration reduction,noise reduction and acoustic switches.The conclusions obtained in this thesis may provide useful guidance for the design and application of hard/soft PCs or acoustic wave devices with tunable band gaps.