Wave Propagation In Two-dimensional Chiral Periodic Lattices

The lattice structures have been attracted extensive investigations and have wide application prospect in the field of civil engineering,mechanical engineering,aerospace engineering,etc,as the structures have distinctive mechanical properties such as the high specific stiffness,high specific strength,extra low weight,fatigue resistance,reduce vibration,active cooling and energy absolving properties and capabilities.The lattice structures are a kind of structures which has a periodic arrangement of unit cells or unicellular.There exists the bandgap characteristics when elastic waves propagate in the periodic structures,which is the natural characteristic of periodic structures.The periodic structures have a very special property which called bandgap characteristics,and the acoustic wave in the bandgap can not propagate.At the same time,as the acoustic wave propagates in the periodic structures,there may exist preferential directions of propagation and energy flow,and the velocity of wave propagation may change.Therefore,the study of wave propagation characteristics in periodic structures is always the frontier of structural engineering,dynamics and control.Based on the above background,this paper investigated the wave propagation characteristics of the two-dimensional square and triangle chiral lattice structures.The unit cells of the two-dimensional chiral lattices structures are composed of rigid rings,lastic slender massless ligaments and local resonators.If the elastic slender massless ligament is rotated clockwise,there will be an angle between the ligament and the line connecting the center of the neighboring rings,and then the structures will obtain the chiral properties.The primary contents of this paper are as following:(1)Building equations of motion.The governing equation of the system can be obtained based on energy variation principle,and the stiffness matrix and the mass matrix of the chiral lattices are deduced with the application of the Bloch’s theory,then,the kinematic model of the system can be obtained.(2)The effect of the chirality angle on the band gaps.The band structures of the square and triangle chiral lattices with different chirality angles will be calculate,respectively.And the effect of the chirality angle on the location and the width of the band gaps will be analyzed.The dispersion relations of the first two modes of the square and triangle chiral lattices with different chirality angles will be calculate,respectively.It can be found that the value of the chirality angle has a significant effect of the width and location of the band gap.Meanwhile,the phase surface also be influenced strongly by the chirality angle.(3)Effect of the chirality angle on the phase and group velocities.The phase and group velocities of the first two modes of the square and triangle chiral lattices with different chirality angles will be calculate,respectively.The dispersion properties of the first two modes will be further researched,and the effect of the chirality angle on the speed and the direction of the propagation of acoustic wave will be obtained.It can be found that the value of the chirality angle has a remarkably effect on the phase and group velocities,the direction of the wave propagation as well as the dispersive characteristic.