Wave propagation in bi-dimensional periodic tensegrity materials and structures

The study of the metamaterials and the phononic crystals is unavoidable for the development of innovative isolation techniques (acoustic, seismic or thermal) thanks to their control properties over the propagation of elastic waves at different wavelength scales. Making use of the spatial periodicity of such materials, it is possible to study the unit cell individually and only subsequently extending the type harmonic plane wave Solution of the equations of motion to the whole domain by applying the Floquet-Bloch theorem. In this thesis we study the dispersion curves obtained in the cases of one-dimensional and two-dimensional lattices through scripts in Matlab. Thus we obtain the characteristic band diagrams of the dispersion curves of these materials (pass band, stop band, bandgap and fano resonance). In particular, the present work focuses on the study of a lattice whose cells are tensegrity structures modeled as a reticular structure with the lamped mass approach: the study is reduced to the simplest case of two-dimensional monoatomic lattice. From the dynamic analysis of this model we obtain the dispersion curves of the pre-tension variation in the elements.