Coupling effects of nonlocal and modified couple stress theories incorporating surface energy on analytical transverse vibration of a weakened nanobeam

Abstract

An analytical solution to the flexural vibration of a weakened nanobeam on the basis of the nonlocal modified couple stress theory including surface effects is under consideration. In this investigation nanobeams are studied within the framework of the Euler-Bernoulli beam theory. The nanobeam is weakened by a crack modeled as a rotational spring at the crack position. This assumption divides the beam into two sections, invoking additional conditions on the beam. The governing equations and boundary conditions for the beam are obtained by applying the Hamilton principle. The natural frequencies for the cracked nanobeam are determined to investigate the effects of crack severity, crack position, nonlocal parameter, material length scale parameter and surface effect parameters. It has been found that the mentioned parameters have considerable effects on stiffness and have a significant impact the dynamic behavior of the nanobeam.