Research On Characteristics Of Vibration In Finite Waveguide Structures

Elastic metamaterial(EMM)is recognized as a new type of artificial composite medium assembled by specific micro-structure unit cells.Thanks to these unit cells’ local monopolar or multi-polar resonance,the elastic wave propagating in these composite mediums is manipulated and presents rich and striking phenomenon,which can not exist in homogenized composing materials.When applying metamaterial into practical application,the corresponding structures should be finite thereby the focus will become the analysis of these vibration characteristics.Therefore,for typical EMM waveguides,it is necessary to set up proper methods for vibration analysis and investigate deeply these particular modal distributions and relevant vibration features.In this thesis,the vibration analysis methods for EMM rod,beam and corresponding sandwich structures are set up in three aspects including inherent feature,steady vibration and transient vibration,based on the idea of equivalent.And based the methods,the corresponding vibration features different from homogenized structure are also demonstrated.The main work are concluded as follow:Firstly,in term of inherent feature,based on the effective medium theory,EMM rod,beam and sandwich structure are equivalent as the corresponding effective medium structure,and then starting from their classical theory,the changes in natural frequency and modal of these structure by the frequency dependence and negative feature of effective density are deeply demonstrated,and further these underlying mechanisms are revealed from the view of forming of standing wave.Finally,by modelling the EMM structure from unit cell scale by Finite Element Method(FEM),the above analyses and results are validated.Secondly,by equaling those finite structures including EMM rod,beam and sandwich structures as the corresponding effective medium structures based on above equivalent process,these steady responses are calculated,and then simulations from unit cell scale are implemented for validation of the theoretical analysis.Thirdly,in term of transient vibration,the above continuous systems that is EMM rod,beam and sandwich structure are simplified the discrete systems,and then their control equations are constructed through Lagrange equation and calculated numerically by Runge-Kutta methods to acquire the transient response.In addition,Genetic Algorithm(GA)is applied to optimize the dimensions of the EMM structures to acquire the better transient performance.Finally,in term of experimental validation,samples of EMM rod,beam and sandwich structure are fabricated and the relevant experiment platforms are set up to validate their vibration features including buffer,band gap and particular distribution of natural frequencies.The study shows,firstly,influenced by scatterers’ dipolar resonance or frequency dependence of effective density,the inherent features of these EMM finite waveguide structures are distinctive from the homogenization,including the specific corresponding relations of modals before and after band gaps,specifically which is the n-th modal shapes before and after band gaps are identical in macroscopic scale;the absence of natural frequencies within band gap;natural frequencies gather densely around frequency at lower edge of band gap.Secondly,EMM finite waveguide structures have distinctive shock resistance,and this feature can be attributed to the behaviors of energy storage of attached subsystems.Thirdly,in term of analysis of inherent and steady vibration,the effective medium theory adapted can give concise predictions,and for the transient vibration,discretizing methods are also adaptable.Finally,the features including buffer regarding shock loads,band gap and particular distribution of natural frequencies are validated experimentally.