Scale-dependent free vibration analysis of carbon nanobeam with non-ideal boundary condition

A simply supported damped Euler-Bernoulli beam with immovable end conditions is considered. The concept of non-ideal boundary conditions is applied to the beam problem. In accordance, the boundaries are assumed to allow small deflections and moments. Governing equations of system are derived through Hamilton’s principle and then the problem is solved by Lindstedt – Poincare technique and derived natural frequency. Finally, the influences of the nonlocal parameter, perturbation parameter and aspect ratio on the free vibration characteristics of the nanobeams are discussed in details.