This study addresses the problem of predicting convergence outcomes in Duffing equation, a nonlinear second-order differential equation. The equation exhibits intriguing behavior both undamped free vibration and forced with damping, making it subject significant interest. In vibration, result oscillates randomly between 1 −1, contingent upon initial conditions. For multiple variables, including...

In this note, small amplitude free vibration of a double-beam system in presence of inner layer nonlinearity is investigated. The nonlinearity is due to inner layer material and is not related to large amplitude vibration. At first, frequencies of a double-beam system with linear inner layer are studied and categorized as synchronous and asynchronous frequencies. It is revealed that the inner l...

The Adomian Decomposition Method (ADM) has been applied to a wide class of problems in physics, biology and chemical reactions. The method provides the solution in a rapid convergent series with computable terms. This method was successfully applied to nonlinear differential delay equations [1], a nonlinear dynamic systems [2], the heat equation [3,4], the wave equation [5], coupled nonlinear p...

The exact solutions of both the cubic Duffing equation and cubic-quintic are presented by using only leaf functions. In previous studies, have been proposed functions that integrate in phase trigonometric Because they not simple, procedures for transforming complicated convenient. first derivative function can be derived as root. This factored. These factors or multiplications to equation. Some...