Bandgap And Damping Property Analysis Of Two-dimensional Periodic Composite Structure Based On PWE

The research object in this paper is 2-dimenstional periodic elastic composite material. The dispersion relations demonstrates the property of band structure when the elastic or acoustic wave propagate in it, it means that the wave of such frequency located in the band-gap will be forbidden to propagate, so it have became to be a focus point to study recent years as one kind of functional material which be used to damp vibration and noise. Because the calculation of natural frequency is just needed in the bandgap calculation process, the damping consideration of each component is not be considered in such process, but the damping of material is avoidless in the process of wave propagation, so this paper principally study the damping property when elastic or sound wave propagates in such material. This job is based on the plane wave expansion method which is the most popular method in the bandgap calculation, the elastic parameters such as the material density, wave velocity and damping factor are all expanded based on PWE method, then the expansion type of the wave propagation equation in such damping material is obtained in this paper. Finally the damping coefficient is induced based on principal modes method of vibration, then the damping performance of the material with different kinds of structure can be assessed by the damping coefficient. The damping properties of the square and triangle point matrix structure are calculated in this paper, respectively. The relationship between the natural frequency and the corresponding damping coefficient is shown when the same and the several filling fractions, respectively. It finds that the damping coefficient is directly proportional to not only wave frequency, but the filling fraction of bigger damping material. It is more important that it shows the damping coefficient of the triangular matrix structure is bigger than the one of the square matrix structure via the compare of both structures. So in practical application such material with the maximum damping effect can be found out in the all kinds of structures with the suitable bandgap by this calculation process.