On the geometrically nonlinear vibration of a piezo-flexomagnetic nanotube

In order to describe the behavior of thin elements used in micro-electro-mechanical systems (MEMS) and nano-electro-mechanical systems (NEMS), it is essential to study a nonlinear free vibration of nanotubes under complicated external fields such as magnetic environment. In this regard, the magnetic force applied to the conductive nanotube with piezo-flexomagnetic elastic wall is considered. By the inclusion of Euler-Bernoulli beam and using Hamilton's principle, the equations governing the system are extracted. More importantly, a principal effect existed in a nonlinear behavior such as axial inertia is thoroughly analyzed which is not commonly investigated. We then consider the effects of nanoscale size using the nonlocal strain gradient theory (NSGT). Hereafter, the frequencies are solved as semianalytical solutions on the basis of Rayleigh-Ritz method. The piezo-flexomagnetic nanotube (PF-NT) is calculated with different boundary conditions. In order to validate, the results attained from the present solution have been compared with those available in the open literature. We realized that the nonlinear frequency analysis is so significant when a nanotube has fewer degrees of freedom at both ends and its length is long.