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The present work aimed to characterize the free vibrations’ behaviour of nanocomposite plates obtained by incorporating graded distributions of carbon nanotubes (CNTs) in a polymeric matrix, considering the carbon nanotubes’ agglomeration effect. This effect is known to degrade material properties, therefore being important to predict the consequences it may bring to structures’ mechanical performance. To this purpose, the elastic properties’ estimation is performed according to the two-parameter agglomeration model based on the Eshelby–Mori–Tanaka approach for randomly dispersed nano-inclusions. This approach is implemented in association with the finite element method to determine the natural frequencies and corresponding mode shapes. Three main agglomeration cases were considered, namely, agglomeration absence, complete agglomeration, and partial agglomeration. The results show that the agglomeration effect has a negative impact on the natural frequencies of the plates, regardless the CNTs’ distribution considered. For the corresponding vibrations’ mode shapes, the agglomeration effect was shown in most cases not to have a significant impact, except for two of the cases studied: for a square plate and a rectangular plate with symmetrical and unsymmetrical CNTs’ distribution, respectively. Globally, the results confirm that not accounting for the nanotubes’ agglomeration effect may lead to less accurate elastic properties and less structures’ performance predictions.

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The influence assessment of carbon nanotubes (CNTs) agglomeration on CNT-reinforced composite (CNTRC) thick plates’ behavior is the main aim of the present work. CNTs are known to agglomerate into clusters even for relatively low volume fractions, which imposes the need to characterize the effects this may introduce in structures behavior, also knowing that recent works have concluded that neglecting agglomeration phenomenon may lead to an overestimation of the mechanical properties of nanocomposites. Hence, it matters to understand how the arising of these clusters may affect the static and free vibrational behaviors of low side-to-thickness nanocomposite plates. To this purpose, the nanocomposite plate properties’ estimation is performed by using the two-parameter model of agglomeration based on the Eshelby–Mori–Tanaka approach, while for behavioral analyses one considers a Higher-order Shear Deformation Theory (HSDT) based on the displacement field of Kant, implemented through the finite element method. The analyses developed consider a set of parametric studies involving the assessment of the influence of side-to-side ratios, side-to-thickness ratios, boundary conditions, and CNTs’ distributions along the thickness. The results obtained allow concluding that the transverse deflections and fundamental frequencies of these structures are significantly influenced by the CNTs’ agglomeration.

An effective head immobilization is an important requirement in radiotherapy treatment sessions, although it may also be thought in the future as a precious aid in brain medical imaging. Thus, the present work is focused on the stiffness optimization of a customized head immobilization mask, modelled upon the head reconstruction surface based on computerized tomography images. This paper proposes a strategy supported by a metaheuristic optimization technique and a metamodeling approach for the whole mask, illustrated at its most unfavorable region occurring in the gnathion region.