Forced vibration of sinusoidal FG nanobeams resting on hybrid Kerr foundation in hygro-thermal environments

Size-dependent forced vibration behavior of functionally graded (FG) nanobeams subjected to an in-plane hygro-thermal loading and lateral concentrated and uniform dynamic loads is investigated via a higher-order refined beam theory, which captures shear deformation influences needless of any shear correction factor. The nanobeam is in contact with a three-parameter Kerr foundation consisting of upper and lower spring layers as well as a shear layer. Hygro-thermo-elastic material properties of the nanobeam are described via power-law distribution considering exact position of the neutral axis. Through nonlocal elasticity theory of Eringen and Hamilton's principle, the governing equations of higher-order FG nanobeams on Kerr foundation under dynamic loading are derived. These equations are solved for simply-supported and clamped-clamped boundary conditions. A detailed parametric study is performed to show the importance of moisture concentration rise, temperature rise, material composition, nonlocality, Kerr foundation parameters, and boundary conditions on forced vibration characteristics and resonance frequencies of FG nanobeams. As a consequence, Kerr foundation parameters lead to a significant delay in the occurrence of resonance frequencies.