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- Nonlocal free vibrations of metallic FGM beamsPublication . Loja, M.A.R.; Rzeszut, Katarzyna; Barbosa, JoaquimThis work aims to analyse the free-vibration response of functionally graded, simply supported beams with different gradient directions, taking into account nonlocal effects. To this purpose, the first-order shear deformation theory and the nonlocal elasticity theory of Eringen are used, in order to assess the influence of size dependency effects on the free-vibration responses of those beams. The influence of other factors such as the aspect ratio of the beams and the evolution of the constituents’ mixture through the beam thickness and along its length is also considered. In this last case, a mixture distribution is proposed, accounting for the boundary conditions’ characteristics. The finite element model is first verified against existing alternative solutions, to assess and illustrate its performance. Based on the conclusions achieved, a set of parametric studies is then developed. The results are discussed considering the material distribution profiles, and conclusions are drawn with respect to their relative performance under the analysed conditions.
- In-plane functionally graded plates: A study on the free vibration and dynamic instability behavioursPublication . Loja, Amélia; Barbosa, JoaquimFunctionally graded materials are well-known composite materials, characterized by a continuously varying mixture of materials' phases, tailored to meet structures operating requirements while contributing to minimize abrupt stress transitions at dissimilar materials' interfaces, as occur in composite laminates. Hence, designing a functionally graded material to comply with these objectives constitutes an important modelling tool to improve structures' functionality. These graded composite materials present more commonly a mixture variation through the structures' thickness direction. However, when dealing with thin structures this solution may present evident limitations, both from the manufacturing perspective as well as from the through-thickness distribution influence on the structure response. It is therefore important to explore other spatial mixture distributions' possibilities. To this purpose, the present work considers thin graded materials' plates which constitution is defined by a set of different in-plane volume fraction distributions. The influence of these distributions on the free vibrations and dynamic instability of thin plates is assessed through a comprehensive set of parametric studies. The free vibration problem and the dynamic instability problem' solutions are respectively obtained by Rayleigh-Ritz and Bolotin's methods. As a complementary analysis contribution, image correlation studies are also developed for a set of fundamental mode shapes.