Temperature Control On The Defect Mode Of Phononic Crystal And Low Frequency Adjustment Of Lamb Wave Band Gap

Phononic crystal have gain attention by more and more scholars with abundant physical connotation and broad application prospects over the past two decades. Phononic crystal is a periodic composite materials or structures with acoustic or elastic wave band. Its main characteristics are:when there is defect mode exists in the phononic crystal, the acoustic wave or elastic wave, which frequency is in the band gaps frequency range, will be localized in the point defect or propagation along the line defect; having phononic band gaps, acoustic wave or elastic wave within the frequency range of the band gap is not allowed to pass. However other frequency range (passband) of elastic wave or elastic wave will be propagated without loss under the effect of dispersion relations. Phononic crystal is a new type of artificial materials. We can control the classic wave frequency by designing the structure or materials. So there are many applications about phononic crystals in reality. For example:designing a new type of high-efficiency filter and waveguide, and so on. Thus, studying and improving the theory and local impact of phononic crystals is very significant.First of all, we set out the natural crystals and photonic crystals, thus, leading to the relative concepts and properties of phononic crystal, and expounded the significance and research status of phononic crystals.Secondly, we introduced the calculation method of the phononic crystal band structure and the common arrangement of two-dimensional phononic crystal. Starting with the Bloch theorem and the basic principles of elasticity, we emphatically introduced the finite element method, and introduced the basic steps of finite element method numerical simulation.And then, we introduced the study of temperature effects on the defect states of two-dimensional phononic crystal in detail. We proposed two novel kinds of new models, Model 1 is constructed by solely changing the temperature of the central defect rod; Model 2 is constructed by changing the temperature of the central defect rod and rotating it to 45 degree. We got some important conclusions:For Model 1, the defect modes will fall in the band gap when the temperature of the central defect rod is lower than Curie temperature as well as the temperature of phononic crystal is higher than Curie temperature, and the lower the defect temperature is, the lower the frequency of the defect mode will be; For Model 2, the defect modes will fall in the band gap as long as the temperature of phononic crystal is higher than Curie temperature, both the number and the frequency of the defect states are related to the defect temperature no matter what the temperature of the defect rod will be. But when the temperature of phononic crystal is lower than Curie temperature, even if the rotated rod has broken the geometry symmetry, there is no defect mode existing in the band gap at all. The influence of heat flow around the central defect rod has also been discussed, and we found that the gradient of temperature due to heat flow just has a little influence on the results and it can be ignored.At last, the numerical investigation of Lamb wave propagation in two-dimensional phononic crystals composed by depositing the heavy cylinder stubs squarely onto both sides of a composite thin plate is presented. Our calculated results show that:Significant enlargement of the relative bandwidth by two orders of magnitude compared to two-dimensional binary locally resonant phononic crystal plates and one order of magnitude compared to both the ternary composite plate and the simple plate with stub structures at deep sub-wavelength scale is obtained and discussed. Based on an efficient finite element method, we show that this band gap enlargement is due to the coupling between the plate mode and ’double mass-spring’ mode, which leads to the enhancement of the locally resonance mechanism. The calculated elastic wave displacement fields illustrate the physics mechanism of the opening of the low frequency band gap and the existing of the flat bands. We also found that both the band gap and the flat bands depend on the geometry parameters of the heavy stubs and composite plate significantly.The innovation of this paper lies in that two novel point defect models and locally resonant phononic crystal plate models are put forward. We can easily obtain the defect mode by this way but not to change the lattice arrangement, shape, filling fraction and materials of the component. Some meaningful results are also found, without change the material component of the phononic crystal plate we can obtain large relative band gap by constructing a new model of phononic crystal plate.