Gul, UfukAydogdu, Metin2024-06-122024-06-1220210263-82231879-1085https://doi.org/10.1016/j.compstruct.2020.113169https://hdl.handle.net/20.500.14551/20576It is known from experimental studies that softening or hardening material behaviours of nanostructures change with the microstructure of the considered material. However, most of the size dependent continuum models (nonlocal stress gradient, strain gradient and couple stress theories) predict only softening or hardening material behaviour. Except of these size dependent theories doublet mechanics predicts both softening and hardening responses of the material like experiments in micro/nano-structures. In the present study, free vibration analysis of functionally graded (FG) periodic structure nanobeams are investigated via doublet mechanics theory. Periodic FG nanobeams are modelled as a simple crystal lattice type. Micro strains and stresses are expanded in Taylor series and obtained micro relations transformed to macro stress-strain relations. Thus, by use of bottom-up approach yields the more physical and accurate analysis of nanostructures in the doublet mechanics model. After deriving the mathematical formulation of a periodic FG nanobeam, vibration problem is examined for general boundary conditions. Ritz method is used in the solution. Adjusting of softening and hardening responses of the material gives a beneficial optimization and design of nanostructures.en10.1016/j.compstruct.2020.113169info:eu-repo/semantics/closedAccessDoublet MechanicsBottom-Up ApproachFunctionally Graded Periodic NanobeamsRitz MethodVibrationFree-Vibration AnalysisBuckling AnalysisStatic AnalysisEulerArticle257Q1WOS:0006047275000142-s2.0-85095579616Q1