Small-scale effects on hygro-thermo-mechanical vibration of temperature-dependent nonhomogeneous nanoscale beams

In this article, hygro-thermo-mechanical vibration analysis of functionally graded (FG) size-dependent nanobeams exposed to various hygro-thermal loadings is performed via a semi-analytical differential transform method (DTM). Three kinds of environmental conditions, namely, uniform, linear, and sinusoidal hygro-thermal loading, are investigated. Temperature-dependent material properties of a nonlocal FG beam change gradually according to the power-law distribution. A size-dependency description of the nanobeam is conducted using the nonlocal elasticity theory of Eringen. Applying DTM, the nonlocal coupled governing equations obtained from Hamilton's principle are solved. Finally, the impacts of moisture concentration, temperature rise, nonlocal parameters, material composition, and slenderness ratio on the vibrational characteristics of nanosize FG beams with arbitrary boundary conditions are explored. These findings can be used for the accurate design of FG nanostructures in various environmental conditions.