Dynamical analysis of a vertical excited pendulum using He’s perturbation method

The current paper investigates the nonlinear dynamics of an excited pendulum by a crank-shaft-slider mechanism (CSSM), in which it is restricted to move vertically. He’s method of homotopy is employed to obtain the analytical solution of the governing differential equation. The numerical solution of this equation is obtained using the fourth-order Runge-Kutta method (RKM). The comparison between both solutions demonstrates a high level of consistency, which confirms the precision of the gained analytic solution. The graphical representations of these solutions are presented to reveal the influence of various parameters on the investigated motion.