Statistical Analysis Of Wave Localization And Delocalization In Randomly Disordered Phononic Crystals With Finite Cells

In recent years,phononic crystals have attracted extensive attention,and a great deal of studies have been focused on the calculation and analysis of phononic crystals.Owing to the interaction between the propagating elastic wave and the periodic structure in phononic crystals,band gaps will be produced.The band structures of elastic waves propagating in phononic crystals have introduced to many potential engineering applications,such as sensors,filters,vibration and noise reduction and so on.In practical applications,due to manufacturing errors during machining production,phononic crystals can not satisfy the completly periodic condition and random disorder is inevitable.In addition,the random disorder will lead to some new phenomena in phononic crystals,which can be used to provide a new theoretical basis and approach for controlling the propagation of elastic waves.Howerver,when the random disorder is considered in phononic crystals,the band structures are randomly disoredered as well.The propagation of elastic waves in randomly disordered phononic crystals has gradually become the focus of research.Firstly,the development and research process of random disordered phononic crystals are introduced in this thesis.The influence of random disorder on phononic crystals and its importance in practical application are expounded.It also emphasizes the necessary of using finite structure to calculate randomly disordered phononic crystals,and also explains the advantages of statistical method.Next,the lumped-mass method in one-dimensional and two-dimensional phononic crystals are introduced in detail.An efficient calculation method based on the lumped-mass method of randomly disordered phononic crystals with finite cells is proposed.Based on the Doolittle method,the dynamic equation is transformed,and the analytical solution of the dynamic equation can be obtained,which does not require the large-scale stiffness equation to be solved.The band structures of one-dimensional and two-dimensional phononic crystals are expressed by amplitude frequency response function.The accuracy and efficiency of the proposed method are illustrated by the analysis of the numerical results.Based on Monte Carlo method,the one-dimensional and two-dimensional random disordered phononic crystals are studied from the statistical point of view.In one-dimensional case,random disorder is introduced into the length and cross-sectional size of epoxy.And in two-dimensional case,random disorder is introduced into the side length and thickness of scatterer respectively.The means,standard deviations and confidence intervals are used to study the influence of random on the band structure of phononic crystals.The effect of the cell number on randomly disordered phononic crystals is also analyzed in this thesis.Furthermore,the optimal groups of control random samples are given,which can make the passband or stopband maximum or minimum.The results show that random disorder can greatly change the band structures in phononic crystals,and the importance of the cell number on phononic crystals is proposed.In addition,an important find in this thesis is that not only localization but also delocalization will occur in random disordered phononic crystals with finite cells.These two phenomena are very important for the application of phononic crystals.Wave localization and wave delocalization have a great impact on practical applications in randomly disordered phononic crystals.