On the modeling and simulation of the nonlinear dynamic response of NEMS via a couple of nonlocal strain gradient theory and classical beam theory

In the present research, the dynamic characteristics of the nanoscale tubes and pipes with nonuniform cross-sections are examined. The aforementioned nanostructures are made by imperfect axially functionally graded materials (AFGM) that compose ceramic and metal phases along the tube length direction, involving the porous voids. To this purpose, the Hamilton principle is implemented to obtaining the governing equation and related boundary conditions using classical beam theory coupled to the nonlinear Von-Karman theory. In order to apply the size impact, the nonlocal strain gradient theory is considered that both hardening and softening parameters are involved. Also, iteration techniques, including the generalized differential quadrature method (GDQM), are used to solve linear and nonlinear derived partial differential equations (PDE). Finally, the obtained results are explained in detail to investigate the impact of nonlinear amplitude, nonlocal and strain gradient parameter, porosity parameter, etc., for both clamped and simply-supported types of boundary conditions, which are helpful to design the nanoelectromechanical structures (NEMS).