Large Amplitude Free Vibration of Nanobeams Subjected to Magnetic Field Based on Nonlocal Elasticity Theory

[[abstract]]In the present study, nonlinear free vibration behavior of nanobeam subjected to magnetic field is investigated based on Eringen's nonlocal elasticity and Euler–Bernoulli beam theory. The Hamilton's principle is adopted to derive the governing equations together with Euler–Bernoulli beam theory and the von-Ka?rma?n's nonlinear strain–displacement relationships. An approximate analytical solution is obtained for the nonlinear frequency of the nanobeam under magnetic field by using the Galerkin method and He's variational method. In the numerical results, the ratio of nonlinear frequency to linear frequency is presented. The effect of nonlocal parameter on the nonlinear frequency ratio is studied; furthermore, the effect of magnetic field on the nonlinear free vibration behavior of nanobeam is investigated