Some Abnormal Wave Propagation Behaviors In Periodic Structures And Their Control

Periodic structures or materials with band gap properties are called phononic crystals(PCs).Band gap is an important branch of phononic crystals research.In recent years,many achievements have been made in the active control of band gap.At the edge of the band gap,the group velocity will change rapidly,which will cause the wave propagation to appear abnormal behaviors.These pass band functionalities on the one hand give birth to various extraordinary wave propagation characteristic which cannot be acquired in normal materials such as negative refraction,directional propagation and so on,on the other hand make wave propagation behaviors easier to be controlled and manipulated.These abnormal behaviors have shown the wonderful application prospects in novel acoustic devices,including sound filters,acoustic mirrors,acoustic wave guides,and vibration isolators.In this thesis,three kinds of abnormal wave propagation behaviors including negative refraction,directional wave propagation and topological edge states are studied.The main contents include: 1.A simplest monoatomic lattice chain is investigated with the weakly nonlinear springs connecting the masses.An active control action represented by the piezoelectric spring is also exerted on every mass.Linear springs between the second-nearest masses are used to model the nonlocal interaction.The one-dimensional monoatomic lattice chain with nonlocal interaction and piezoelectric effect is investigated and the asymptotic solution is obtained through the Lindstedt-Poincaré(L-P)perturbation method.The dispersion relation is derived.Numerical results show that the nonlocal effect can effectively enhance the frequency in the middle part of the dispersion curve.When the nonlocal effect is strong enough,zero and negative group velocities can be evoked at different points along the dispersion curve,and this provides different ways of transporting energy including forward-propagation,localization and backwardpropagation of wavepackets relative to the phase velocity.Both the nonlinear effect and the active control can also enhance the frequency,but neither is able to produce the zero or negative group velocities.Specifically,the active control enhances the frequency of the dispersion curve including the point where the reduced wave number equals zero and therefore gives birth to a nonzero cutoff frequency and a band gap in the low frequency range.With a combinational adjustment of all these effects,the wave propagation behaviors can be comprehensively controlled and energy transferring can be readily manipulated in various ways.2.The nonlocal effect on wave propagation is further studied for a the two-dimensional(2D)structure.The second-neighbor interactions in non-diagonal directions are included to account for the nonlocal effect.The influences of the spring stiffness in the diagonal directions and the nonlocal effect on the propagation characteristics of elastic waves are then scrutinized.From the dispersion relation curve and the equi-frequency contours,it is seen that when the diagonal spring stiffness and nonlocal effect in xdirections increase,the slope of the second curve in the(38)-M and(38)-X directions will not always be positive,meaning that the negative group velocity occurs.Therefore,an incident wave vector with a chosen angle to the negative group velocity can lead to the negative refraction phenomenon in the two-dimensional mass-spring structure.Another interesting phenomenon called directional radiation of elastic waves can also be achieved by adjusting the nonlocal effect or the stiffness of diagonal springs.Within a certain range,the stronger the nonlocal effect in a specific direction is,the more obviously the elastic waves propagate along this direction.When the stiffness of the springs in diagonal directions is strong enough,the wave will propagate in diagonal directions.In this thesis,we theoretically analyze and numerically simulate the phenomena of negative refraction and directional wave propagation by choosing a proper set of parameters of the two-dimensional mass-spring structure.3.Based on the valley Hall effect,we investigate the acoustic topological insulator or topological metastructure,where an acoustic wave can exist only in an edge or interface state instead of propagating in bulk.Breaking the structural symmetry enables the opening of the Dirac cone in the band structure and the generation of a new band gap,wherein a topological edge or interface state emerges.Further,we systematically analyze two types of topological states: one type is confined to the boundary,whereas the other type can be observed at the interface between two topologically different structures.Results denote that the selection of different boundaries along with appropriately designed interfaces provides the acoustic waves in the band gap range with abilities of one-way propagation,dual-channel propagation,and tunable the output position of the acoustic wave.Furthermore,we show that the acoustic wave propagation paths can be tailored in diverse and arbitrary ways by combing the two aforementioned types of topological states.The frequency range of edge state is adjusted by changing the boundary selection,so that the structure has the filtering characteristics.4.The acoustic experiments are carried out with two different types of boundaries.The results verify that the path of acoustic wave propagation can be controlled by choosing the boundaries.Good agreement between experiments and simulations is obtained when a proper damping coefficient is taken.