Comparative analysis between surrounding viscoelastic media on the buckling characteristics of nanobeams

The static and dynamic responses of axially loaded nanobeams with surrounding viscoelastic media are investigated and discussed. Size-dependent or nonlocal effects are accounted for via Eringen’s nonlocal elasticity theory. Additionally, the system is studied for various boundary conditions including clamped–clamped, clamped-hinged, and hinged-hinged. To study the interaction between the nanobeam and the surrounding media, several viscoelastic media are considered including the two-element Kelvin-Voight and Maxwell models and the three-element Standard Solid I, Standard Solid II, Standard Fluid I, and Standard Fluid II models. The governing equations of motion are obtained via the Euler–Bernoulli beam theory and extended Hamilton’s principle and by considering each viscoelastic medium as a distributed load along the length of the nanobeam. After deriving and nondimensionalizing all governing equations, a static analysis is performed to determine the critical buckling loads for each of the surrounding viscoelastic media. Additionally, a linear dynamic analysis is employed to study the effect of the surrounding medium on the system’s linear natural frequency in the pre- and post-buckling regimes. Finally, an in-depth study on the elastic and viscous coefficients of each model depicts how the changes to these parameters can affect both the static and dynamic responses of the proposed system. A thorough study of axially loaded nanobeams embedded within all six viscoelastic media is not present in the literature, thus motivating this effort.