Successive approximate solutions for nonlinear oscillation and improvement of the solution accuracy with efficient non-perturbative technique

In the present study, several successive approximate solutions of nonlinear oscillator are derived by using efficient frequency formula. A systematical analysis formulation helps to establish a general periodic solution. Each approximation represents, individually, solution oscillator. For optimal design and accurate prediction structural behavior, new optimizer is demonstrated for solutions. The classical Duffing formula has been modified. numerical calculations show high agreement with exact frequency. justifiability obtained confirmed comparison It shown that enhanced large amplitudes not restricted oscillations have small amplitudes. approach can provide perfect oscillation.