Research On The Plate-shell Metamaterials For High-frequency Vibration Attenuation

Vibration widely exists in industrial production,technical research and daily life,such as transportation,aerospace,precision testing,etc.According to vibration function,vibration can be classified as beneficial vibrations or harmful vibrations.Beneficial vibration can realize some functions such as screening materials,cleaning dirt and ultrasonic preparation process,but most vibrations are harmful.High-frequency vibration as a kind of harmful vibration often brings interference with the development of various fields.In the field of testing,the test accuracy of the equipment will be affected by high-frequency vibration,and long-term highfrequency vibration will lead to a degradation in the performance of the equipment.In the field of aerospace,launch vehicles often encounter strong high-frequency vibration shocks during flight,which can lead to reduced reliability or even failure of electronic components.Metamaterials are special structures designed artificially,which can break the limits of natural laws,and achieve extraordinary mass density,elastic modulus and other properties.Compared with traditional vibration isolation materials,metamaterials have the advantages of flexible structure and easy control,which provide a new research direction for high-frequency vibration attenuation.The thesis first introduces the development history of metamaterials and focuses on the research progress of domestic and foreign research on plate-shell elastic wave metamaterials in recent years.Secondly,to obtain the energy band structure,the controlling equations of elastic wave propagation in metamaterials were established by the basic theory of elastic dynamics,and the equation combined with lattice theory and Bloch’s theorem to obtain the dispersion relation equation of the metamaterial.Then,we designed and proposed a notched cross-shaped metamaterial for vibration attenuation requirements in the frequency band of 20 k Hz ～ 100 k Hz.To widen the band gap,the influence of key structural parameters such as lattice constant,thin plate thickness and mass block thickness on the band gap width is analyzed.To enhance the bandgap property,the metamaterial was constructed by arranging 6.5 mm and 13 mm unit cells in the periodical array.The simulation results show that the band gap is in the frequency bands of 19 k Hz ～ 28.6 k Hz,31.5 k Hz ～ 34 k Hz,36.8 k Hz ～ 80.7 k Hz and 81.5 k Hz ～ 99.6k Hz,which makes the band gap cover the target frequency band.Through the kinetic transport experiments,the attenuation amplitude of the sample is measured to be 75% in the target frequency band.To further improve the vibration attenuation effect,based on the single-phase star structure with a wide band gap,we propose an arc-convergent star structure composed of a single material.The energy band structure was calculated and found that there is still a wide passband in the frequency band of 20 k Hz ～ 50 k Hz and 80 k Hz ～ 100 k Hz,and then the sharp-angle convergent star structure is proposed to form a star-shaped plate-shell metamaterial by combining and arranging two structural periods.The transmission response curves of the metamaterial were calculated and showed that the attenuation domain combining the bandgap ranges of arc-convergent star structure and sharp-angle convergent star structure,achieving full coverage of the bandgap within 20 k Hz ～ 100 k Hz.The attenuation amplitude of the sample in the target frequency band is 85% as measured by the dynamical transmission experiment,which significantly improves the vibration attenuation effect in the target frequency band.