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Materials and structural engineering have undergone profound changes over the past few decades, particularly with the emergence of composite materials, which provide outstanding mechanical performance while offering considerable design flexibility. At the same time, controlling the propagation of mechanical waves within structures, especially flexural elastic waves, has attracted growing interest in diverse fields such as nondestructive evaluation, vibration reduction, energy harvesting, and smart sensing. In this context, waveguide structures represent a particularly promising area. They enable the channeling, filtering, or focusing of waves along specific directions, and can therefore be exploited to design advanced devices for detection, transmission, or damping. When implemented using composite materials, these structures benefit from additional anisotropy and flexibility, opening new opportunities for tailoring dispersion and vibrational behavior. However, designing such structures poses several challenges. The expected performance, in terms of wave guiding, focusing, or attenuation, depends strongly on the mechanical properties of the materials, the geometry of the structure, and a range of uncertain parameters such as environmental variability, aging, and boundary conditions. Under these circumstances, conventional deterministic design approaches may prove inadequate, often leading to devices that are sensitive to deviations between nominal and actual operating conditions. This highlights the importance of adopting a robust design methodology that explicitly accounts for parameter variability from the outset, ensuring reliable device performance across a broad spectrum of scenarios. This thesis addresses these challenges by developing a methodology and decision-support tools for the robust design of composite structures used as flexural elastic waveguides. The proposed methodology is applied to the design of a graded-index lens (GRIN Lens) for focusing flexural elastic waves in a composite plate of constant thickness. The design is experimentally validated on a prototype fabricated from unidirectional composite material.