Perturbation-iteration method for strongly nonlinear vibrations
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Abstract
The new perturbation iteration method developed by Pakdemirli and co-workers for regular problems is extended to cover problems with blow up secularities for sufficiently long time intervals. The Duffing equation, the quintic Duffing equation, systems with quadratic and cubic nonlinearities and systems with odd nonlinearities are treated using the new approach. In all cases, the perturbation parameter and/or the nonlinearity coefficients are selected to be large so that the system is strongly nonlinear. Approximate analytical solutions are presented and contrasted with the numerical solutions. It is concluded that the method outlined is reliable for strongly nonlinear equations having constant-amplitude type solutions.