A unified formulation for dynamic analysis of nonlocal heterogeneous nanobeams in hygro-thermal environment

In this article, combined effect of moisture and temperature on free vibration characteristics of functionally graded (FG) nanobeams resting on elastic foundation is investigated by developing various refined beam theories which capture shear deformation influences needless of any shear correction factor. The material properties of FG nanobeam are temperature dependent and change gradually along the thickness through the power-law model. Size-dependent description of the nanobeam is performed applying nonlocal elasticity theory of Eringen. Nonlocal governing equations of embedded FG nanobeam in hygro-thermal environment obtained from Hamilton’s principle are solved analytically. To verify the validity of the developed theories, the results of the present work are compared with those available in the literature. The effects of various hygro-thermal loadings, elastic foundation, gradient index, nonlocal parameter, and slenderness ratio on the vibrational behavior of FG nanobeams modeled via various beam theories are explored.