Abstract:

We developed a multiple scattering method for the calculation of the frequency band structure of a phononic crystal consisting of non-overlapping elastic spheres arranged periodically in a host medium of different elastic properties. Using a variation of the same method we can also calculate, with the same ease and accuracy, the coefficients of transmission, reflection and absorption of elastic waves incident on a slab of the material of finite thickness. The elastic coefficients of the spheres and/or the host medium can be complex and frequency dependent. We demonstrate the effectiveness of the method by applying it to specific examples.