Study On Vibration Characteristics Of Magnetorheological Elastomer Metamaterial Sandwich Beam

Acoustic metamaterials are artificial subwavelength periodic composite structures with extraordinary acoustic or mechanical properties.The unique structural design gives them some characteristics that natural materials do not have such as negative equivalent mass density and negative equivalent bulk modulus.Locally resonant acoustic metamaterials have overcome the limitation of generating low-frequency band gaps in small structures,this characteristic provides a new way for low-frequency vibration suppression.The band gap range of traditional acoustic metamaterials is usually determined once the structural design was complete,and the band gaps do not have tunability.On this basis,researchers have tried to introduce smart materials into the design of acoustic metamaterials to develop metamaterials with adjustable vibration characteristics.Based on the band gap theory of locally resonant acoustic metamaterials and the active control method,this study proposed a magnetorheological elastomer sandwich metamaterial beam with tunable band gaps in low frequency.Theoretical analysis and finite element simulation of its vibration characteristics and elastic wave tunability are studied.The main work and research results are as follows:The vibration characteristics of a magnetorheological elastomer sandwich beam are studied.Firstly,the theoretical analysis model of magnetorheological elastomer material is introduced,and the transverse motion equations of magnetorheological elastomer sandwich beam under an external magnetic field are derived through Hamilton’s principle.The magnetorheological elastomer is treated as a linear viscoelastic material,and the vibration characteristics of the magnetorheological elastomer sandwich beam under various boundary conditions with an external magnetic field are obtained.The band gap characteristics and transmission characteristics of magnetorheological elastomer sandwich metamaterial beams are studied.Based on the locally resonant band gap mechanism,an acoustic metamaterial beam with periodic magnetorheological elastomer sandwich beam-mass resonators is proposed.The band gaps of the metamaterial beam are calculated based on the mass-spring model.Furthermore,the tunable band gaps of the magnetorheological elastomer metamaterial beam are discussed and analyzed.Finally,the influence of material parameters and structural parameters on the transmission characteristics of the metamaterial beam is discussed.The results show that the band gaps of the magnetorheological elastomer metamaterial beam move to the high-frequency range with the increment of the applied magnetic field.With the consideration of the damping effect of the magnetorheological elastomer,the attenuation amplitude in the band gaps of the magnetorheological elastomer metamaterial beam decreases,while the frequency range of the acceleration response attenuation increases.The acceleration response attenuation range of the magnetorheological elastomer metamaterial beam moves to the high-frequency range with the increment of the core layer thickness of the resonator.The transmission characteristics of magnetorheological elastomer acoustic metamaterial beams with defects are studied.A magnetorheological elastomer acoustic metamaterial beam with defect configuration is constructed by applying different external magnetic flux densities at a certain cell.The effects of defect location,external magnetic flux density,defect cell resonator core layer thickness and defect cell resonator end mass on the transmission characteristics of defect configuration metamaterial beam are analyzed.The results show that the transmission loss reflecting the defect configuration is generated in the acceleration response attenuation range of the defect configuration metamaterial beam,and the vibration localization occurs at the corresponding transmission loss frequency.In addition,the transmission characteristics of the defect configuration metamaterial beam are not affected by the change of the point defect position.The transmission loss frequency moves to the highfrequency range with the increment of the external magnetic flux density,moves to the highfrequency range with the increment of the resonator core layer thickness of the defect unit cell,and moves to the high-frequency range with the decrease of the resonator end mass of the defect unit cell.The above results provide a theoretical guide for the design of magnetorheological elastomer acoustic metamaterials and the regulation of elastic wave transmission.