Free vibration analysis of FGM framed nanostructures using variational-consistent boundary conditions

This paper analyses free vibrations of framed nanostructures made Functionally Graded Material (FGM) based on the Nonlocal Elastic Theory (NET) and Dynamic Stiffness Method (DSM). FGM characteristics vary nonlinearly throughout height beam element. The NET considers nonlocal parameter that perfectly captured size effect nanostructures. However, makes paradoxes in bending vibration behaviour with ends. To overcome these phenomena, nanostructure is modelled according to Euler–Bernoulli theory variational-consistent boundary conditions have been derived. exact solutions differential equations motion are found using DSM. influences nonlocal, material, geometry parameters Pasternak’s foundation then analyzed. It shown study can be applied other FGMs as well more complicated structures.