Vibrations of an Euler-Bernoulli Nanobeam on a Winkler/Pasternak-Type Elastic Foundation

A non-local Euler-Bernoulli nanobeam theory is used to calculate free vibrations for a beam resting on a Winkler/Pasternak-type elastic foundation. On using Hamilton's Principle, the nonlinear equation of motion, which includes terms for stretching of the neutral axis, is derived. The Adomian modified decomposition method is applied to solve the fourth-order governing equation. Investigations are made of the effects on the vibrations of the non-local parameter, the Winkler and Pasternak parameters, in addition to the effects of applying simple-simple and clamped-clamped boundary conditions.