Nonlinear coupled mechanics of functionally graded nanobeams - Gholipour, Alireza; Ghayesh, Mergen H. (International journal of engineering science, 2020)
Addressed in this article, as the first attempt, is the forced coupled nonlinear mechanics of functionally graded (FG) nanobeams subject to dynamic loads via developing a high-dimensional model. A geometric nonlinear Euler-Bernoulli theory is used to define the displacement distribution. To incorporate small-size influences a nonlocal strain gradient theory (NSGT) scheme, possessing two independent length scale characteristics, is employed. The FG material distribution is on the basis of the Mori-Tanaka homogenisation technique. The two-parameter constitutive relation is used and the corresponding potential energy is formulated considering the variation nature of the material properties. The energy due to the motion of the nanobeam is also formulated and nanobeam's energies are dynamic-wise balanced by the work of the external dynamic loading; this is performed in the framework of Hamilton's principle. The coupled transvers/axial motion equations in the nonlinear regime are obtained. In the framework of a weighted residual method, the truncated/discretised model is obtained and numerically solved for force/frequency diagrams for nonlinear mechanics analysis. For a simple linear version of the problem, a linear analysis is also performed via the finite element method for verification purposes.