Illustration of the homotopy perturbation method to the modified nonlinear single degree of freedom system

Abstract

Nonlinear Single degree of freedom (SDOF) systems are crucial for understanding the behavior of various real-world systems, designing and analyzing mechanical and dynamical systems. In this article we have modified the SDOF model by introducing the nonlinearity as well as damping with/without external force and applied the homotopy perturbation method (HPM) to explain its various phenomena. We have compared the analytical solutions obtained via the HPM to the provided numerical results by the fourth-order Runge-Kutta (RK4) method for verifying the precision and validity of the solutions. The presentation and explanation of the dynamic results can add a new dimension to the research field by influencing the importance of nonlinear SDOF systems.