Thermally induced nonlinear dynamic analysis of temperature-dependent functionally graded flexoelectric nanobeams based on nonlocal simplified strain gradient elasticity theory

Abstract

In this work, thermally induced dynamic behaviors of functionally graded flexoelectric nanobeams (FGFNs) are analyzed theoretically while considering the neutral surface concept and the von Karman nonlinearity induced by thermal environment. The temperature field is assumed to vary only in the thickness direction by solving a simple steady state heat transfer equation and to be constant in the plane of the beam. The temperature-dependent material properties of FGFNs are assumed to vary continuously throughout the thickness according to a power-law form. For such FGFNs, the nonlocal simplified strain gradient elasticity theory to capture the effect of size-dependent and, the higher order shear deformation beam theory to account for rotary inertia and transverse shear strains are adopted to formulate the governing equations and associated boundary conditions, which are solved by using a two-step perturbation method. In the numerical part, comparison study is also performed to verify the present theoretical model and the parametric analysis is systematically studied. It is also found that the thermally induced bending amplitude, nonlinear frequency and frequency ratio depend enormously on the material distribution profile, the flexoelectricity, the size-dependent effect and the imposed temperature field.