Ruta, GiuseppeEroğlu, Uğurcan2023-03-062023-03-062022Eroğlu, U., & Ruta, G. (2022). Approximate closed-form solutions for vibration of nano-beams of local/non-local mixture. Meccanica, 57(12), 3033–3049. https://doi.org/10.1007/s11012-022-01612-7‌256455https://hdl.handle.net/20.500.11779/1892https://doi.org/10.1007/s11012-022-01612-7This paper presents an approach to natural vibration of nano-beams by a linear elastic constitutive law based on a mixture of local and non-local contributions, the latter based on Eringen's model. A perturbation in terms of an evolution parameter lets incremental field equations be derived; another perturbation in terms of the non-local volume fraction yields the variation of the natural angular frequencies and modes with the 'small' amount of non-locality. The latter perturbation does not need to comply with the so-called constitutive boundary conditions, the physical interpretation of which is still debated. The possibility to find closed-form solutions is highlighted following a thorough discussion on the compatibility conditions needed to solve the steps of the perturbation hierarchy; some paradigmatic examples are presented and duly commented.eninfo:eu-repo/semantics/openAccessNatural vibrationConstitutive boundary conditionsNano-beamsPerturbation methodsNon-local elasticityArticle10.1007/s11012-022-01612-72-s2.0-85142699132N/AN/A3033-304957WOS:000889032000001