A numerical study on the buckling and vibration of nanobeams based on the strain and stress-driven nonlocal integral models

Abstract

In this paper, the free vibration and buckling behaviors of nanoscale beams with different boundary conditions are analyzed using the integral formulation of Eringen’s nonlocal elasticity theory. To this end, both strain- and stress-driven nonlocal integral models are employed. The nanobeams are modeled according to the Euler–Bernoulli beam theory. Moreover, a novel numerical approach is proposed for solving the obtained governing equations. By this numerical method, which uses matrix differential and integral operators, the integral governing equation is directly solved and the difficulties related to converting the integral governing equation into the differential one are bypassed. Comparisons are made between the predictions of strain and stress-driven models about the vibration and buckling responses of nanobeams subject to various end conditions. The results indicate that based on the stress-driven model, the frequency and critical buckling load increase with increasing the nonlocal parameter, whereas they decrease when the strain-driven integral model is used.