| The quality of noise and vibration is one of the important indicators to measure the development of modern scientific and technological equipment,and the essence of structural vibration and noise radiation lies in the mutual coupling between the acoustic/elastic wave propagation effect and the surrounding medium.Therefore,regulating the acoustic/elastic wave behavior in the structure is an effective way to realize the vibration and noise reduction of the structure.Recently,radial metamaterials constructed based on the cylindrical coordinate system have introduced new ideas for wave propagation control in structures,and have been confirmed by researchers to have more excellent band gap characteristics,whichprovides a new opportunity for ultra-low frequency vibration reduction and noise reduction technology in the engineering field.In addition,the omnidirectional wave barrier and wave regulation properties exhibited by radial metamaterials are expected to provide new theories and methods for seismic isolation and shock absorption design of existing major urban buildings and important facilities in the field of earthquake engineering.In this paper,on the basis of in-depth analysis of the propagation laws and dispersion characteristics of elastic and seismic waves,a quasi-static I-shaped radial elastic metamaterial with a zero-frequency initial band gap is designed by means of theoretical modeling,experimental testing,and numerical calculation.A stepped radial elastic metamaterial with the coupling effect of local resonance and Bragg scattering is proposed,and radial metamaterial is introduced into the field of seismic engineering.The propagation characteristics of seismic Lamb waves and surface waves in radial metamaterials are further proposed.The layered radial seismic metamaterial provides a scientific basis for the design of radial periodic structures in engineering and seismic fields.The main research contents are as follows:(1)In order to obtain the zero-frequency initial bandgap,an "I"-shaped radial elastic metamaterial(IREM)is proposed,and the propagation characteristics of elastic waves under different confinement states are studied.Through the calculation and study of the dispersion relation,frequency response function and eigenmode displacement field,it is found that the zero-frequency initial wide energy bandgap of 0-16849 Hz can be generated in the double-sided confinement state,which is mainly caused by the modal transition caused by the confinement effect,and the equivalent mass-spring model is applied to reveal its mode transition mechanism.Furthermore,by studying the directional vibration displacement field of the finite periodic structure,it is found that the mechanism of the zero-frequency initial band gap is the local resonance mechanism.Next,build a vibration test experimental platform to verify the existence of ultra-low frequency broadband.The research conclusions can be applied to engineering fields such as ultralow frequency vibration reduction.(2)A novel stepped radial elastic metamaterial(SREM)is proposed,and its structure is periodically arranged in a stepped shape along the radial direction.The propagation characteristics of Lamb waves in structures are studied,and modal visualization methods are applied to explore wave attenuation and shielding mechanisms.Compared with traditional radial elastic metamaterials,the degeneracy in the SREM energy band structure is separated,which can open ultra-low frequency and ultra-wide band gaps,the total bandwidth is 75 times that of traditional radial elastic metamaterials,and the wave attenuation ability is enhanced more than 70%.The introduction of the stepped array enhances the low-frequency local resonance effect,and opens the ultra-low frequency broadband of its structure under the coupling effect with the Bragg scattering effect.Further,the effects of structural parameters and central hole shape on the band gap characteristics are discussed.As the step angle increases,the structural Lamb wave mode and the structural local resonance coupling strength change,resulting in the overall shift of the energy band structure to low frequencies;with the increase of porosity,the localization degree in the structure changes,and the band gap characteristics show complex fluctuations.Based on this model,the experimental samples were processed,and the vibration propagation characteristics of the experimental samples were tested to prove their ultra-low frequency broadband characteristics.(3)Introducing radial metamaterials into the field of earthquake damping for the first time,and proposing a new type of ultra-low frequency broadband radial seismic metamaterial(RSM)whose structure is periodically embedded in the soil by a steel ring to realize the omnidirectional shielding of seismic Lamb waves and surface waves.The finite element method is used to study the propagation characteristics of seismic waves in RSM.Compared with traditional seismic metamaterials,RSM has lower and wider band gap properties for both seismic Lamb waves and surface waves.For seismic Lamb waves,the onset frequency of the band gap of the RSM with rectangular cross-section is as low as 1.6 Hz,the bandwidth ratio is as high as 81.27%,and its bandwidth is increased by 65.33% compared with the same type of seismic metamaterial.For surface waves,the relative bandwidth of RSM can reach 57.5%,which is caused by the coupling between the axial resonance of the structure and the Rayleigh mode.In addition,a 3D full-scale finite period model including in-plane and out-of-plane modes is designed to verify the seismic wave shielding properties of the RSM.The proposed shielding method can provide new theories and methods in the field of seismology and related fields of ultralow frequency vibration damping or explosion protection.(4)Further,a novel radial seismic metamaterial(LRSM)based on the layered theory is proposed,whose unit cell structure is optimized as a multi-layer ring and is distributed in a radial periodic array.The dispersion relation and displacement vector field of LRSMs with different layers are studied,and it is found that there are ultra-low frequency broadband characteristics in the range of 0.1-20 Hz,which is produced by the coupling of local resonance and surface wave modes.Comparing three LRSMs with different numbers of layers,it is found that the initial frequency and bandwidth do not change monotonically with the increase of the number of layers.When there are two layers of LRSMs,there is an optimal band gap,and the relative bandwidth can reach 83.9%.Further,the effects of structural geometric parameters and circumferential continuity on the band gap characteristics are discussed,and the frequency domain analysis and threedimensional transient wave propagation analysis of finite periodic structures are carried out.Finally,through time-frequency analysis,it is verified that LRSM can effectively attenuate seismic surface waves of 0.1-20 Hz,and its maximum amplitude attenuation can exceed 85%.The novel periodic structure proposed in this paper can provide new options for the fields of earthquake and low-frequency vibration reduction.The purpose of this paper is to promote the application of radial metamaterial theory to problems such as ultra-low frequency vibration control and seismic design in engineering,and to provide new theoretical basis and design guidelines for mechanical and seismic engineers. |
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