Study On Mechanical And Electromagnetic Dynamic Characteristics Of Materi/als With Periodic Structures

Material with periodic structures is a kind of structural body formed by more than two kinds of materials with different parameters, which alternate periodically in space. As a novel type engineering material, it is becoming a matter of concern for more and more people. Some parameters of material with periodic structures alternate periodically in the scale of electromagnetic wave or elastic wave. Due to the action of the periodic structures, the material has bandgaps. Study on bandgaps plays a very important role in material with periodic structures. It has abundant physical meaning and broad prospect of application.The finite-difference time-domain method (FDTD) is one of the most powerful numerical methods for the modeling of the electromagnetic wave, elastic wave and acoustic wave propagation and scattering. It is based on the discretization of partial-differential wave equations. The partial-differential equations are transformed to finite-difference equations by the discretization in the time and the space. Consequently, the relation of field components and time in the discret points is obtained in the process of wave propagation. In the paper, the theory of FDTD method in electromagnetic and elastic field is studied, and two-dimensional and three-dimensional difference cells and equations are established. Numerical stability of the method also discussed.When computing the field with the FDTD method, the determination of absorbing boundary condition is an important aspect. Firstly, this paper deduces the impedance matched condition of perfectly matched layer in electromagnetic field. Secondly, PML model for evolution problem in elastic field is discussed from the viewpoint of elastodynamic. A very high damping parameter and a small layer width are obtained. It can control the transmission coefficient in a very small range while achieving a quasi-perfect absorption of the incident wave.Finally, square structure model of two-dimensional periodic material is developed. Based on the difference equations, programs are developed to calculate the transmission coefficient in ГX and ГM direction of electromagnetic and elastic periodic structures, and the gap spectra are obtained. Additionally, bandgaps of periodic structures with negative Poisson's ratio and linear defect structures are analyzed. One of characteristics for FDTD method is convenient for visualization. Wave propagation was simulated in periodic and linear defect structures. Differences are compared between the wave propagation in the pass bands and bandgaps at...