Free Vibration and Buckling Analyses of Nanobeam Embedded in Pasternak Foundation

In this paper, free transverse vibration and buckling analyses of a nanobeam are presented by coupling the Euler-Bernoulli beam (EBT) theory and Eringen’s nonlocal elasticity theory. The nanobeam is embedded in the Pasternak foundation. Hamilton’s energy principle is used to derive governing differential equations. The Lagrange polynomial-based differential quadrature method (PDQM) and a harmonic differential quadrature method (HDQM) are used to convert the governing differential equation and boundary conditions into a set of linear algebraic equations. The first three frequencies and the lowest critical buckling loads for clamped-clamped, clamped-simply supported, and simply supported-simply supported boundary conditions are obtained by implementing the bisection method through a computer program written in C++. The impacts of nonlocal Eringen’s parameter (scaling effect parameter), boundary conditions, axial force, and elastic foundation moduli on frequencies are examined. The effects of nonlocal Eringen’s parameter, boundary conditions, and elastic foundation moduli on critical buckling load are also studied. A convergence study of both versions of DQM is conducted to validate the present analysis. A comparison of frequencies and critical buckling loads with those available in the literature is presented.