A sixth-order compact finite difference method for vibrational analysis of nanobeams embedded in an elastic medium based on nonlocal beam theory

In the present paper, the free vibration characteristics of nanobeams embedded in an elastic medium are investigated. Inclusion of size effects is considered in the analysis by incorporating Eringen’s nonlocal elasticity continuum into the classical Euler–Bernoulli beam theory. To include the surrounding elastic medium, the Pasternak elastic foundation model is utilized, including shear deformation of the elastic medium. A high-order compact finite difference method (CFDM) is employed for sixth-order discretization of the nonlocal beam model to obtain the fundamental frequencies of nanobeams corresponding to three commonly used boundary conditions, namely simply supported–simply supported, clamped–clamped, and clamped–free. Numerical results are presented to indicate the accuracy of the method based on the sixth-order discretization for predicting the vibrational response of embedded nanobeams subject to various boundary conditions.