A new perturbation algorithm for strongly nonlinear oscillators
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Date
2009
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Abstract
A new perturbation algorithm combining the Method of Multiple Scales and Lindstedt-Poincare techniques is proposed. The algorithm combines the advantages of both methods. Convergence to real solutions with large perturbation parameters can be achieved for both constant amplitude and variable amplitude cases. Three problems are solved: Linear damped vibration equation, classical duffing equation and damped cubic nonlinear equation. The new method does not violate the main assumption of perturbation series that correction terms should be much smaller than the leading terms. It is proven that for arbitrarily large perturbation parameter values, correction terms remain much smaller that the leading terms. Results of Multiple Scales, new method and numerical solutions are contrasted. The proposed new method produces much better results for strong nonlinearities.
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Keywords
Control nonlinearities , Constant amplitude , Correction terms , Damped vibrations , Duffing equations , Leading terms , Method of multiple scale , Multiple scale , Numerical solution , Perturbation parameters , Perturbation series , Real solutions , Strong nonlinearity , Strongly nonlinear oscillator , Variable amplitudes , Algorithms