A new analytic solution for buckling of doubly clamped nano-actuators with integro differential governing equation using Duan–Rach Adomian decomposition method

• A new analytical solution for nano-actuators in a general form is obtained.
• Duan–Rach modified Adomian decomposition method is applied.
• Duan's fast convergence parameter is utilized.
• The analytical solution is free of any undetermined coefficient.
• Explicit relations between non-dimensional parameters is obtained.

The Duan–Rach modified Adomian Decomposition Method (ADM) is utilized to obtain a convergent series solution for buckling of nano-actuators subject to different nonlinear forces. To achieve this purpose, a general type of the governing equation for nano-actuators, including integro-differential terms and nonlinear forces, is considered. The adopted governing equation for the nano-actuators is a non-linear fourth-order integro-differential boundary value equation. A new fast convergent parameter, Duan's parameter, is applied to accelerate the convergence rate of the solution. The obtained solution is an explicit polynomial series solution free of any undetermined coefficient. Thus, it can facilitate the design of nano-actuators. As a case study, the results of the approach are compared with the results of Wazwaz Modified Adomian Decomposition Method (MADM) (with undetermined coefficients) as well as a numerical method. The results indicate the remarkable robustness of the present approach.