Accurate Buckling Analysis of Magnetically Affected Cantilever Nanoplates Subjected to In-plane Magnetic Fields

Abstract

Cantilever-based nanostructures have attracted widespread attention in nanoengineering. As key components of cantilever-based nanosensors, some cantilever nanoplates are exposed to magnetic fields in working conditions. This paper performs the buckling analysis of magnetically affected cantilever nanoplates resting on elastic foundations. The aim of the presented research is to discuss the effects of magnetic fields on the buckling characteristics of cantilever nanoplates. Based on Eringen’s nonlocal elasticity theory, the exact buckling solutions of the cantilever nanoplates are obtained by using symplectic approach incorporating a superposition technique. To resolve the difficulties in dealing with the complex boundary value problems of cantilever nanoplates, the buckling problem is divided into two sub-problems which can be analytically solved by the symplectic approach. Exact solutions of the buckled cantilever nanoplate are derived by a superposition of the obtained solutions for sub-problems. Comparisons are presented to show the accuracy and stability of the proposed method. Parametric studies of the in-plane magnetic field and elastic foundation on the buckling characteristics of cantilever nanoplate are also given. Highly accurate critical buckling loads and buckling mode are derived analytically. This study has shown that applying magnetic field is an effective way to control the critical buckling loads and buckling mode shapes of cantilever nanoplates.