Bloch–Floquet waves in flexural systems with continuous and discrete elements

• Propagation of flexural waves in bi-coupled periodic structures is studied.
• Structures consist of continuous and discrete phases in series and in parallel.
• Propagation zones are presented in the invariant and physical spaces.
• Systems allowing for full propagation in both directions are presented.
• Applicability of tuned mass dampers is extended to broadband filtering.

In this paper we describe the dynamic behavior of elongated multi-structured media excited by flexural harmonic waves. We examine periodic structures consisting of continuous beams and discrete resonators disposed in various arrangements. The transfer matrix approach and Bloch–Floquet conditions are implemented for the determination of different propagation and non-propagation regimes. The effects of the disposition of the elements in the unit cell and of the contrast in the physical properties of the different phases have been analyzed in detail, using representations in different spaces and selecting a proper set of non-dimensional parameters that fully characterize the structure. Coupling in series and in parallel continuous beam elements and discrete resonators, we have proposed a class of micro-structured mechanical systems capable to control wave propagation within elastic structures.