The Directional Characteristics Of Wave Propagation In Two-dimensional Periodic Structures

Periodic structures own the distinctive feature of wave forbidden characteristic of attenuation zones. Waves cannot propagate through the periodic mediums when the frequencies of elastic waves are in the attenuation zones. Moreover, even though the frequencies of elastic waves are out of the attenuation zones, periodic structures with a particular design can have the directional characteristics of elastic waves propagation. That means the energy of elastic waves mostly flow in certain directions, and few or cannot flow in other directions. With the attenuation zones and the directional characteristics of wave propagation, we can design two-dimensional periodic structures which have the capacity of vibration reduction or isolation. Thus these periodic structures can be used in environmental vibration reduction and seismic isolation in Civil Engineering.In recent years, some scholars have proposed types of hole structures to reduct environmental vibration, and conduct experiments on these structure. However, from the point of periodic theory, this model actually is a two-dimensional periodic structure which consists of the hole and soil. In this paper, based on the periodic theory of solid-state physics, the directional characteristics of two-dimensional periodic structures are studied by using the group velocity method. Specifically, the theoretical analysis and numerical simulation are conducted in this paper. The first, this paper studies the dispersion curves of two-dimensional periodic structures with finite element method. The second, we get the group velocity with numerical calculation. At last, the numerical simulation of hole-soil periodic structures are studied by finite element method with reasonable models and boundary conditions. The content are as follows.(1) We study the directional attenuation zones of periodic structure with group velocity on the base of solid-state physics theory.(2) Both in-plane and out-of-plane directional attenuation zones of periodic structure are investigated and the affecting factors on attenuation zones are analyzed. The research reveals elastic modulus of soil, the hole radii and the periodic constant have an important influence on the attenuation zones of periodic structure.(3) We study the directional propagation characteristics of elastic waves whose frequencies are out of directional attenuation zones with dispersion curves and calculating group velocity. (4) The numerical simulation of in-plane vibration are studied by reasonable models to reflect the directional characteristics with frequencies of elastic waves both in and out of directional attenuation zones. Furthermore, we can provide a reference for design in practical reduction of enveronmental vibration.