Theoretical Analysis And Experimental Study On The Vibration Gap Of One Dimensional Phonon Crystal

Phonon crystal is an elastic composite material composed by different elastic units arranged in a periodical sequence. The band gap appears as elastic waves propagate in it. The research of the band gap structure of the phonon crystal is, therefore, of great importance for both theoretical studies and applications, and has aroused great concern among research institutions and scholars all over the world.In this paper, the elastic dynamic analysis method is used to analyze the vibration band gaps and the dynamic response of the finite one-dimensional phonon crystal rod. The results show that: the interactions of the phonon crystal material and elastic waves make waves of certain frequencies have no corresponding vibration mode in periodic structures, that is to say, they can't spread, and thereby band gaps appear. Based on this, the corresponding displacement response mode between the band gap and pass band is given.Firstly, the finite element method is adopted to study the performance of the limited periodic composite phonon crystal structure, and the mathematical model is discretized. The conclusion is same with the result calculated from the elastic dynamic analysis. Secondly, the interpretation of the vibration band gaps is given in terms of vibration mechanics. Periodic structures caused the periodic changes of the stiffness matrix and mass matrix, which in turn caused the adjustment of resonance points of the phonon crystal system, so that there is no resonance points in some continuous frequency domains of the whole range. Thus vibration band gaps appear. Based on this, a theory of the resonance point band gaps different from the Bloch scattering mechanism and local resonance band gaps is proposed.The lattice length, the materials components ratio and the elastic modulus and density of the two materials of the phonon crystal structure is adjusted respectively. By computational analysis, the influence on the system vibration band gaps caused by the change of the phonon crystal structure parameters is obtained.By using the home-made samples, and conducting tests combined with ultrasonic detector, the existence of vibration band gaps of the phonon crystal is verified from an experimental viewpoint.