Analysis Of Elastic Wave Band-gap And Damping Property In3-dimensional Lattice Composite Material

In recent years, with the rapid development of material science and technology, simple lightweight has no longer met our needs, and people urgently need to find new materials, which have many excellent properties including light weight, energy absorption and noise reduction. Lattice composite material has many good performances such as high specific stiffness, high specific strength, vibration reduction, sound absorption and so on. It is an ordered ultra-light porous composite material and has broad application in the field of transportation, aerospace, construction and so on. The periodic micro cubic truss composite material is constructed on periodic micro truss structure for the skeleton, its internal voids are filled with a kind of damping material and different mass balls, in this way a kind of3-dimensional lattice composite material comes into being, which is one kind of structure-function composite materials. So far, except our work, we don’t find any other researches on band-gap and damping property of periodic micro-truss composite materials with balls.The paper researched elastic wave band-gaps and damping properties of periodic composite materials with micro cubic truss structure and balls from the two aspects of infinite and finite period, by using the ways of theoretical analysis and numerical simulation; and offered some numerical examples as well as verified the feasibility and effectiveness of the theoretical approach. The main contents and conclusions are as follows:For the infinite periodic structure, we use the Floquet-Bloch theory to derive the formulae of applying periodic boundary conditions on the representative unit cell under the case of proportional damping. After establishing differential equations without damping, a set of calculation program was developed to solve the complex coefficient eigenvalue equations and the band-gaps and damping properties are obtained. The results show that periodic micro cubic truss/four balls composite material has better damping effect in the low frequency range. For the periodic micro cubic truss/double balls composite materials, the greater density sum of mass balls, the larger wave propagation attenuation coefficient, the lower frequency of band-gaps and the better performance of vibration absorption within a certain range.For the finite periodic structure, taking the periodic micro cubic truss/lead ball and steal ball composite material for an example, established finite element model, calculated its transmission characteristics in950-1000Hz and1000-1050Hz frequency ranges by harmonic response analysis and researched elastic wave propagation in periodic structural composite materials. Then, we analyzed band-gaps of the composite material. The results show that the first direction and the second direction band-gaps calculated in the condition of finite periodic structure are almost the same with what has been calculated under the case of infinite periodic structure.