Study On Propagation Mechanism Of The Interface Wave In Elastic Metamaterials

Elastic Metamaterial(EMM)is a kind of new artificial metamaterial composed of complex microstructures.Due to the monopole and multipole localized eigenmodes of the unit cell,EMMs have shown a series of specific dynamic characteristics differrent from the component material and greatly expand the space of the existing material properties.EMMs have some unique elastic wave control properties,which are mainly attributed to the embedded subwavelength scatterers.According to effective-medium theory,the complex wave behaviors in EMMs can be described appropriately when the size of scatterer is far smaller than the wavelength(i.e.,under the long wavelength limit).Existing studies have shown that the effective parameters of an EMM are generally frequency-dependent and can become negative neighbor the vibrational eigenmodes' frequency of the scatterer.People have recognized the frequency dependence and negative characteristics of the effective-medium parameters may lead to peculiar elastic wave behaviors,and the properties of body waves in EMMs have been studied extensively.However,investigation for the elastic wave near the boundary or interface is still in a primary stage.The classic theory manifests some types of surface or interface wave for natural mediasuch as the well-known Rayleigh,Lamb and Love waves.When it comes to EMMs,it is not difficult to imagine that the similar surface/interface waves may also exist under certain conditions,since EMMs can be regarded as an extension of natural medium from the perspective of effective medium.According to effective-medium theory,I studied the mechanisms of interface waves travelling in EMMs,mainly focusing on the forming conditions and transmission characteristics of the interface waves.Details of the work are listed as follows:First of all,the Rayleigh wave phase velocity equation is established.For the different values of effective parameters and wave velocities,the root distributions of Rayleigh wave phase velocity equation are analyzed at great length,and the effective-medium parameter combinations raleted to positive real root are obtained.Furthermore,the influence of effective density,shear modulus and longitudinal wave modulus on Rayleigh wave mode are investigated.A finite element model is constructed by using effective-medium parameters and the actual microstructures,respectively,to verifity the theoretical results.Secondly,the propagation of traveling Lamb wave in single layer of elastic metamaterial is investigated.We categorized the traveling Lamb wave modes inside an elastic metamaterial layer according to different combinations(positive or negative)of effective medium parameters.Then the impacts of the frequency dependence of effective parameters on dispersion characteristics of traveling Lamb wave are studied.Distinct differences could be observed when comparing the traveling Lamb wave along an elastic metamaterial layer with one inside the traditional elastic layer.We further examined in detail the traveling Lamb wave mode supported in elastic metamaterial layer,when the effective P and S wave velocities were simultaneously imaginary.It was found that the effective modulus ratio is the key factor for the existence of special traveling wave mode,and the main results were verified by FEM simulations from two levels: the level of effective medium and the level of microstructure unit cell.Thirdly,the propagation of SH wave in jointed half-spaces composed of EMMs is concerned.According to the dispersion relations,the effects of negative effective medium parameters on the properties of SH wave traveling near the interface are analyzed at great length.It is found that SH wave can always appear and travel along the interface under specific conditions of effective parameter combination,no matter whether the effective transverse wave velocity is imaginary or not.This observation is significantly different from the classic case(jointed half-spaces composed of natural media).Finally,a semi-infinite space model overlied by an EMM-layer is constructed to investigate the existence of Love wave mode travelling in the overlying layer.Based on the dispersion equation,the possible traveling wave solutions of the dispersion equation with different effective-medium parameters are discussed,and the domain of effective-medium parameter corresponding to the Love wave mode is obtained.According to different wave numbers(real or imaginary)of SH wave in the thickness direction and the combinations(positive or negative)of effective-medium parameters,the travelling wave mode are studied in detail,moreover,the Love wave mode curves are calculated by using numerical analysis software.I briefly demonstrate the effect of EMM with typical frequency-dependent effective density on traveling Love wave dispersion characteristics,and the impacts of the negative effective parameters on dispersion characteristics of traveling wave mode are further examined.To conclude,on one hand,the existing EMM theory framework is expanded and enriched,on the other hand,the above works can provide instructive information for the design of EMMs,especially in the field of EMM-based elastic wave isolation and object protection.