Nonlocal Euler-Bernoulli Theory Research Articles

A study of longitudinal magnetic field effect on critical buckling loads of SWCNT embedded in Kerr medium using nonlocal Euler-Bernoulli theory

A study of longitudinal magnetic field effect on critical buckling loads of SWCNT embedded in Kerr medium using nonlocal Euler-Bernoulli theory

Analytical analysis for the forced vibration of CNT surrounding elastic medium including thermal effect using nonlocal Euler-Bernoulli theory

This article studies the free and forced vibrations of the carbon nanotubes CNTs embedded in an elastic medium including thermal and dynamic load effects based on nonlocal Euler- Bernoulli beam. A Winkler type elastic foundation is employed to model the interaction of carbon nanotube and the surrounding elastic medium. Influence of all parameters such as nonlocal small-scale effects, high temperature change, Winkler modulus parameter, vibration mode and aspect ratio of short carbon nanotubes on the vibration frequency are analyzed and discussed. The non-local Euler-Bernoulli beam model predicts lower resonance frequencies. The research work reveals the significance of the small-scale coefficient, the vibrational mode number, the elastic medium and the temperature change on the non-dimensional natural frequency.

Exact solution for large amplitude flexural vibration of nanobeams using nonlocal Euler-Bernoulli theory

In this paper, nonlinear free vibration of nanobeams with various end conditions is studied using the nonlocal elasticity within the frame work of Euler-Bernoulli theory with von K´arm´an nonlinearity. The equation of motion is obtained and the exact solution is established using elliptic integrals. Two comparison studies are carried out to demonstrate accuracy and applicability of the elliptic integrals method for nonlocal nonlinear free vibration analysis of nanobeams. It is observed that the phase plane diagrams of nanobeams in the presence of the small scale effect are symmetric ellipses, and consideration the small scale effect decreases the area of the diagram.

Closed-Form Solutions for Nanobeams Based On the Nonlocal Euler-Bernoulli Theory

Closed-Form Solutions for Nanobeams Based On the Nonlocal Euler-Bernoulli Theory

Non-conservative instability of cantilever carbon nanotubes resting on viscoelastic foundation

In this study, the influence of viscoelastic foundation on the non-conservative instability of cantilever Carbon nanotubes (CNTs) under the action of concentrated follower force is investigated. The Kelvin–Voigt, Maxwell and Standard linear solid types of viscoelastic foundations are utilized to model the interaction between CNT and surrounding viscoelastic medium. The governing equations of motion and boundary conditions are obtained based on the nonlocal Euler–Bernoulli theory using Hamilton's principle. Applying the Galerkin approach, the resulting equations are transformed into a set of eigenvalue equations. The validity of the present analysis is confirmed by comparing the results with those obtained in literature. The effects of the main parameters on the stability characteristics of the CNT are also elucidated. Most results presented in this paper have been absent from the literature for the instability of the CNT subjected to follower force.