Study On Vibration Propagation Characteristics Of Periodic Structure Of Two-dimensional Cellular Micro-truss

With the rapid development of aerospace and modern industry,the requirements for material properties in engineering applications have become increasingly stringent,which has also prompted the enthusiasm for research on composite materials.Metamaterials are a kind of special composite materials.The specific structures built by artificial trusses can be ordered periodically to obtain some unique mechanical properties.The pentamode metamaterial is a new kind of acoustic metamaterial and has a great application prospect in the preparation of acoustic cloaks.It can obtain better materials through the design of the cell structure parameters of the pentamode material and design anisotropic properties to achieve the regulation of wave propagation.Therefore,the research on the static performance of pentamode material is important for the further design and optimization of materials.For the pentamode acoustical metamaterials,exploring the relationship between their structural parameters and their static parameters is of great significance for designing materials with special functions.At present,the asymptotic homogenization method is commonly used to predict the static mechanical parameters in the low-frequency range of periodic structural materials.The transient response method is used to analyze the propagation characteristics of the wave in pentamode materials.In this paper,a periodic two-dimensional honeycomb micro-truss structure is studied as the research object,mainly to study the influence of the geometric structure and material composition of its unit cell on its mechanical parameters,and to explore the geometric parameters and the unit cell static of the structure by using the asymptotic homogenization method.Combining the transformation acoustics proposed by Norris et al.and the design method of the cyclonic acoustic cloak,the coordinate transformation equation in the cylindrical coordinate system is selected.Based on the unit cell static parameters calculated by asymptotic homogenization method,a two-dimensional circular acoustic cloak is constructed,and the stealth effect of the designed two-dimensional acoustic cloak is verified by a finite element full displacement field simulation.The results show that under the condition that the ratio of wavelength to unit cell satisfies certain conditions,the propagation path of the wave in the cloak can be effectively controlled by changing the distribution of physical properties of the structure,so that it can still maintain the original propagation after by passing the obstacle cavity.Using the equivalent parameters which are calculated by asymptotic homogenization method can be well applied to the design of the acoustic cloak.