Wave Propagation Through Multi-layered Structure Accounting For Micro-structural Effects

Along with the development of technology and materials,more and more materials with artificial micro-structure appears.According to large quantities of experiments and phenomena,classical elasticity is nolonger adequate to describe the mechanical behavior of micro-structural materials.Especiallly in dynamic problems,when the wave length and the characteristic length is at the same magnitude,the micro effects and dispersive nature are evidently significant.To be more accurate in the description of micro-deformation of micro-structural materials,the micropolar elasticity,microstretch elasticity and chiral elasticity are considered.Several problems are investigated based on these theories,i.e.,reflection of elastic waves at the viscoelastically supported boundary of micropolar half-sapce,reflection and transmission of elastic wave through micropolar slab sandwiched by elastic half-spaces,reflection and transmission of elastic wave through microstretch slab between two microstretch half-spaces,Bloch wave propagation in one-dimenssional micorpolar phononic crystals,reflection and transmission of plane wave at the chiral-achiral interface and through a chiral slab.The detailed research are listed as follows:(1)The serial and parallel spring-dashpot models are used to simulate the viscoelastically supported boundary.By introduction of weight factor d,the pure elastic boundary and pure viscous boundary are deduced when d equals to 0 and 1,respectively.Separated into in-plane and anti-plane situations,the amplitude of reflection waves with respect to incident wave are calculated by a set of algebraic quations for serial and parallel models,repectively.Then,based on numerical results,the influences of elastic coefficient and viscous coefficient upon phase shift and energy reallocation are investigated.At last,the energy conservation are checked to validate the accuracy of the numerical results.(2)The problem of reflection and transmission of elastic wave through a micropolar slab sandwiched by two elastic half-spaces are investigated.Because the particles in traditional elasticity can not hold micro rotation and couple stress,the boundary condition should be established into two sets.By the analysis of multiple reflection and transmission,the clearer physical picture is presented for the wave propagation through micropolar slab and the formation of resulting waves.Based on numerical results,the influences of non-dimensional thickness of slab and micropolar parameters upon the reflection and transmission coefficients are discussed.(3)The problem of elastic wave propagation through a microstretch slab between two microstretch half-spaces is investigated.Due to different situations,the bilateral half-spaces can be degenerated into micropolar medium and classical elastic medium gradually.Then,the boundary conditions should be modified correspondingly.Based on the numerical cases,the influences of microstretch parameters and non-dimensional thickness on reflection and transmission coefficients are investigated.(4)The propagation of Bloch waves in one-dimensional micropolar phononic crystals are investigated.The investigation are separated into in-plane and anti-plane cases.Based on Bloch theorem and perfect boundary conditions,the transfer matrixes are deduced for each cases,respectively.Then,the dispersive equations can be obtained.The localization factor can be found by analysis of lyapunov exponents and in perfect match with band gap information of phononic crystals.The reflection and transmission coefficients of multi-layers are obtained by stiffness matrixes and the transmission coefficients are also well matched with band gaps which is a validation for the theoretical analysis.Based on the numerical results,the influences of apparent wave number and micropolar effects upon dispersive curves and band gaps are discussed.(5)The reflection and transmission of elastic waves at achiral-achiral interface and through a chiral slab are investigated.Because of the existence of left circularly wave and right circularly wave,the assumption of existence of circularly waves is established.Indeed,the left/right circularly wave in classical elastic medium is coupled by SV wave and SH wave in individual type.Based on the numerical results,the influence of chiral character on reflection and transmission coefficients are discussed.By the detailed investigation mentioned above,the propagation of elastic wave through multi-layer structure are studied theoretically and can be used as theoretical instructor for the acoustic application of materials with micro-structure.