Vibration analysis of Euler-Bernoulli nanobeams embedded in an elastic medium by a sixth-order compact finite difference method

This paper presents an efficient sixth-order finite difference discretization for vibration analysis of a nonlocal Euler-Bernoulli beam embedded in an elastic medium. The Pasternak elastic foundation model is utilized to represent the surrounding elastic medium. Nonlocal differential elasticity of Eringen is exploited to reveal the nun-locality effect of nanobeams. Sixth-order accuracy schemes are developed for discretization of both the governing equation and boundary conditions. Sixth-order accuracy schemes are derived for simply supported, clamped and free boundary conditions. Numerical results include comparison with exact solutions and with previously published works are presented for the fundamental frequencies. In addition, numerical results are presented to figure out the effects of nonlocal parameter, slenderness ratios, and boundary conditions on the dynamic characteristics of the beam.