A new mixed method for nonlinear fuzzy free vibration analysis of nanobeams on nonlinear elastic foundation

A new mixed method for nonlinear fuzzy free vibration analysis of nanobeams on nonlinear elastic foundation is introduced. The governing equations are derived based on the first-order shear deformation theory (FSDT) in conjunction with the von-Kármán’s assumptions and the Eringen’s nonlocal elasticity theory. The differential quadrature method (DQM) is employed to discretize the governing equations and the related boundary conditions. The direct displacement control iterative method is used to solve the discretized system of equations. The fuzzy transformation method (FTM) is coupled with the solution to incorporate effects of different uncertainties such as the small scale effect parameter, nonlinear elastic foundation parameters and vibration amplitude of the nanobeam. Applicability, rapid rate of convergence and high accuracy of the presented method are shown and significant effects of the nonlinearity on the response of nanobeams are investigated via solving some examples.