Spatially periodic structures are used in many fields of science and technology. Examples of such structures are vibration and acoustic isolators made of functionally graded composite materials, trusses of bridges, railway tracks, and similar. Tailoring and optimizing parameters of these structures, which control their dynamic behavior, is a relevant technological challenge. The purpose of the project is to investigate to which extent dynamic characteristics of periodic structures and structures made of the composite materials may be changed and tailored by modulating parameters of the structural composition, and how this could be used in synthesizing new types of structures. Particularly the possibilities to employ the coupled spatial-temporal modulations will be studied.