In this article, small scale effects on free vibration analysis of non-uniform nanobeams is discussed. Small scale effects are modelled after Eringen’s nonlocal elasticity theory while the non-uniformity is presented by exponentially varying width among the beams length with constant thickness. Analytical solution is achieved for free vibration with different boundary conditions. It is shown th...

This paper investigates the natural frequency, steady-state resonance and stability for the transverse vibrations of a nanobeam subjected to a variable initial axial force, including axial tension and axial compression, based on nonlocal elasticity theory. It is reported that the nonlocal nanoscale has significant effects on vibration behavior, which results in a new effective nonlocal bending ...

Abstract A novel formulation of the weak form quadrature element method, referred to as locally adaptive is proposed develop elements for nonlinear graded strain gradient Timoshenko and Euler–Bernoulli nanobeams. The equations motion are obtained based on Hamilton principle while accounting position physical neutral axis. use Gauss points ensure full integration variational statement. develops ...