Civalek, ÖmerUzun, BüşraYaylı, Mustafa Özgür2024-06-132024-06-132021-09-070939-1533https://doi.org/10.1007/s00419-021-02032-xhttps://link.springer.com/article/10.1007/s00419-021-02032-xhttps://hdl.handle.net/11452/42111Buckling analysis of nanobeams with deformable boundary conditions is researched within the framework of doublet mechanics. This theory is an alternative nanomechanics theory for continuum modeling of the granular micromaterials. Doublet mechanics theory takes into consideration the small size parameter due to dealing with also granular nanosized structures. In many studies, rigid supporting conditions are explored in the nanomechanical analysis of beams. Even though the supporting conditions are accepted as undeformable, it is not possible to provide the desired rigidity in practice. A few studies have been conducted to explore the effects of deformable boundaries. In the present work, Fourier sine series as well as Stokes' transformation are utilized to attain the eigenvalue formulation and eigenvector characteristics of the problem. The combination of these two methods is a new approach in applied mechanics; at the same time, it is planned to create a bridge between rigid and deformable boundary conditions. By solving various examples, the accuracy of the proposed method has been tested and an excellent agreement has been achieved with the literature. In addition, the effect of the springs in the boundaries on the critical buckling load has been examined and given in a series of graphs.eninfo:eu-repo/semantics/closedAccessWalled carbon nanotubesFree-vibrationNonlocal elasticityDynamic instabilityAxial vibrationSandwich platesStressFormulationCompositeContinuumDoublet mechanicsNanobeamsDeformable boundary conditionsEigenvalue problemFourier sine seriesScience & technologyTechnologyMechanicsArticle00069348260000147654782911210.1007/s00419-021-02032-x1432-0681