A hardening nonlocal approach for vibration of axially loaded nanobeam with deformable boundaries

Abstract

The dynamic response of nanobeams has attracted noticeable attention in the scientific community. Boundary conditions and other effects on the element are very important in the dynamic behavior of these elements. To the authors' knowledge, there is no paper that provides a general solution for the vibration of a nanobeam with deformable boundary conditions and subjected to a point load according to the hardening nonlocal approach. The present study reports an efficient solution method based on the Stokes' transformation which can investigate the impacts of deformable boundary conditions and axial point load on the transverse vibration of a nanobeam restrained with lateral springs. In this study, an eigenvalue problem obtained by using Fourier sine series and Stokes' transform can be used to easily analyze the frequencies of nanobeam applications subjected to vibration and axial force at both rigid and non-rigid boundaries. It is seen from the presented problem that axial load intensity, nanoscale parameter, boundary condition and length are important variables in the vibration of nanobeams. Also, it should be noted here that the present analytical method can be applicable to a variety of nanotechnology structures and machines, especially micro-electromechanical systems and nano-electromechanical systems.