Nonlinear vibration analysis of the nanobeams subjected to magneto-electro-thermal loading based on a novel HSDT

Abstract

This paper studies the nonlinear vibration analysis of the nanobeams subjected to magneto-electro-thermal loading based on a novel higher-order shear deformation theory (HSDT). Nonlocal elasticity theory is applied to consider the small-scale effect. The nonlinear equations of motion are derived using Hamilton’s principle. First, a Galerkin-based numerical method is utilized to decrease the nonlinear governing equation into a set of Duffing-type time-dependent differential equations. Then, the analytical solutions are obtained based on the method of multiple scales (MMS) and perturbation technique. All of the mechanical properties of the beam are temperature-dependent. The impacts of the several variables are examined on the nonlinear frequency ratio of the nanobeams. The results illustrate that when the maximum deflection is smaller/greater than 0.2, its impact on the nonlinear frequency ratio will decrease/increase.