Research On Vibration Characteristics Of Elastic Metamaterial Plates

Elastic metamaterials(EMs)are man-made functional composites constructed by special sub-structural units arranged in lattice form.Owing to the monopole and multipole localized eigen modes of these units,the composites can show a series of unique dynamic properties and elastic wave regulation capabilities which its component materials do not have.When the concept of EM is introduced into plates and their composite structures commonly used in practical engineering,the vibration problems of such finite metamaterial waveguide structures are mainly concerned.Therefore,it is necessary to study and establish a general vibration analysis method and process for a typical EM plate,and investigate deeply its unique modal characteristics and steady-state forced vibration characteristics,which are different from those of the traditional homogeneous medium.In this paper,the EM plate and its composite plate structure laminated with traditional homogeneous plate are studied.Based on the band structure theory and the effective medium theory(EMT),the band gap(BG)characteristics,inherent characteristics and steady-state forced vibration characteristics of EM plates are studied comprehensively and deeply,and a simplified solution method and framework suitable for vibration analysis of such structures are established.The main work of this paper are as follows:1)In terms of BG characteristics,the band structure of elastic metamaterial plate is solved by using the band structure theory,and the BG characteristics of flexural wave are obtained according to the vibration modes of single cell,which provides a basis for analyzing the inherent characteristics and steady-state forced vibration characteristics of elastic metamaterial plate.2)In terms of inherent characteristics,based on the EMT,the EM plate,EM sandwich plate and EM laminated plate are equivalent as the corresponding effective medium plate and effective medium composite plate.Then,the flexural vibration analysis method of such EM plate structures is established based on the classical vibration analysis theory of various plates.The influence of different dispersion behaviors of effective medium parameters on the modal characteristics is investigated in depth,and the formation mechanism of these laws is revealed from the perspective of flexural wave propagation.Finally,the finite element models with effective-medium parameters and actual unit cell are constructed respectively to verify the reliability of the theoretical prediction by simulation.3)In terms of steady-state forced vibration characteristics,based on the effective medium model and the effective medium composite model established in the analysis of the inherent characteristics,the steady-state forced vibrations of the EM plate,EM sandwich plate and EM laminated plate are investigated in depth by means of the general wave analysis method of the corresponding classical structures.The displacement transmissibility of the metamaterial plates is obtained,and the special displacement field distribution at the resonance peak is summarized.Finally,the theoretical analysis results are verified by FEM simulation from the unit cell level and the equivalent medium level.4)In terms of experimental verification,the samples of EM plate,sandwich plate and laminated plate are fabricated,and the corresponding experimental support device is designed.According to the existing conditions,the experimental platform is built and the frequency response curves of the metamaterial plates are measured,which verified the propagation characteristics of flexural wave in the metamaterial plate from the experimental level.Through the study of the vibration characteristics of EM plates in this paper,a general analysis method and process for the inherent characteristics and steady-state vibration characteristics is established based on the EMT,which provides a simple and quick analytical means and reference for the vibration problems solving of such finite EMs,and enriches the existing research system and framework of EMs.Moreover,the unique vibration characteristics of EM plates obtained in this paper,such as the absence of natural frequencies in the BG range,the unique modal correspondence before and after the BG and the sharp attenuation of the transmissibility in the BG range,provide useful inspiration and reference for the modal characteristic space extension and practical engineering applications of EMs.