Applications of bloch expansion to periodic elastic and viscoelastic media

摘要

AbstractWe consider an unbounded, elastic non homogeneous material with periodic structure. It is shown that the solution of the equations of motion can be expanded in eigenfunctions of periodic operators. The Bloch expansion is used to prove that when the wave‐length is long compared to the period of the structure (related to a small parameter ϵ), the first term of the exact solution expansion, in powers of ϵ, is the solution of the equations obtained in homogenization theory. The case of a long memory linear viscoelastic material is then stud